Transform-based image coding method and device therefor

ABSTRACT

An image decoding method according to the present document comprises the step of deriving modified transform coefficients by applying LFNST to transform coefficients, wherein the step of deriving the modified transform coefficients comprises the steps of: deriving a variable indicating whether an effective coefficient is present in a DC component of a current block; and parsing an LFNST index on the basis of whether the variable indicates that the effective coefficient is present in a position other than the DC component, wherein the variable may be derived on the basis of an individual transform skip flag value for a color component of the current block.

BACKGROUND OF THE DISCLOSURE Field of the Disclosure

The present disclosure relates to an image coding technique and, moreparticularly, to a method and an apparatus for coding an image based ontransform in an image coding system.

Related Art

Nowadays, the demand for high-resolution and high-quality images/videossuch as 4K, 8K or more ultra high definition (UHD) images/videos hasbeen increasing in various fields. As the image/video data becomeshigher resolution and higher quality, the transmitted information amountor bit amount increases as compared to the conventional image data.Therefore, when image data is transmitted using a medium such as aconventional wired/wireless broadband line or image/video data is storedusing an existing storage medium, the transmission cost and the storagecost thereof are increased.

Further, nowadays, the interest and demand for immersive media such asvirtual reality (VR), artificial reality (AR) content or hologram, orthe like is increasing, and broadcasting for images/videos having imagefeatures different from those of real images, such as a game image isincreasing.

Accordingly, there is a need for a highly efficient image/videocompression technique for effectively compressing and transmitting orstoring, and reproducing information of high resolution and high qualityimages/videos having various features as described above.

SUMMARY

A technical aspect of the present disclosure is to provide a method andan apparatus for increasing image coding efficiency.

Another technical aspect of the present disclosure provides a method andan apparatus is to provide a method and apparatus for increasingefficiency of LFNST index coding.

Still another technical aspect of the present disclosure is to provide amethod and an apparatus for increasing coding efficiency of an LFNSTindex based on a transform skip flag.

In an aspect, an image decoding method performed by a decoding apparatusis provided. The method includes: deriving modified transformcoefficients by applying LFNST to transform coefficients, wherein thederiving the modified transform coefficients includes deriving avariable indicating whether a significant coefficient exists in a DCcomponent of the current block and parsing an LFNST index based on thevariable indicating that the significant coefficient exists at aposition other than the DC component, and the variable may be derivedbased on an individual transform skip flag value for color components ofthe current block.

The variable may indicate that the significant coefficient exists at aposition other than the DC component based on the transform skip flagvalue for the color component being 0.

The variable may be initially set to 1 in a coding unit level of thecurrent block, if the transform skip flag value is 0, the variable maybe changed to 0 in a residual coding level, and the LFNST index may beparsed based on the variable being 0.

The transform skip flag for the current block may be signaled for eachcolor component.

The deriving the modified transform coefficient may further includesetting a plurality of variables for the LFNST based on the LFNST indexbeing not 0 and whether the individual transform skip flag value for thecolor component is 0.

If a tree type of the current block is a single tree, the variable maybe derived based on a transform skip flag value for a luma component, atransform skip flag value for a chroma Cb component, and a transformskip flag value for a chroma Cr component.

If a tree type of the current block is dual tree luma, the variable maybe derived based on a transform skip flag valued for a luma component.

If a tree type of the current block is dual tree chroma, the variablemay be derived based on a transform skip flag value for a chroma Cbcomponent and a transform skip flag value for a chroma Cr component.

According to one embodiment of the present disclosure, an image encodingmethod performed by an encoding apparatus is provided. The methodincludes: applying LFNST to derive modified transform coefficients fromthe transform coefficients, applying a plurality of LFNST matrices tothe transform coefficient to derive a variable indicating whether asignificant coefficient exists in a DC component of the current block,selecting the most optimal LFNST matrix among the LFNST kernels based onthe variable indicating that the significant coefficient exist at aposition other than the DC component, and deriving the modifiedtransform coefficient based on the selected LFNST matrix, and thevariable may be derived based on an individual transform skip flag valuefor the color component of the current block.

According to still another embodiment of the present disclosure, theremay be provided a digital storage medium that stores image dataincluding encoded image information and a bitstream generated accordingto an image encoding method performed by an encoding apparatus.

According to yet another embodiment of the present disclosure, there maybe provided a digital storage medium that stores image data includingencoded image information and a bitstream to cause a decoding apparatusto perform the image decoding method.

Advantageous Effects

According to the present disclosure, it is possible to increase overallimage/video compression efficiency.

According to the present disclosure, it is possible to increaseefficiency of LFNST index coding.

According to the present disclosure, it is possible to increase codingefficiency of an LFNST index based on a transform skip flag.

Effects that can be obtained through specific examples of the presentspecification are not limited to the effects listed above. For example,various technical effects that a person having ordinary skill in therelated art can understand or derive from the present specification mayexist. Accordingly, specific effects of the present specification arenot limited to those explicitly described in the present specification,and can include various effects that can be understood or derived fromthe technical characteristics of the present specification.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

FIG. 4 is a diagram exemplarily illustrating a structure diagram of acontent streaming system to which the present disclosure is applied.

FIG. 5 is a diagram schematically illustrating a multiple transformtechnique according to an embodiment of the present disclosure.

FIG. 6 is a diagram exemplarily illustrating intra-directional modes of65 prediction directions.

FIG. 7 is a diagram for describing an RST according to an embodiment ofthe present disclosure.

FIG. 8 is a diagram illustrating a sequence of arranging output data ofa forward primary transform into a one-dimensional vector according toan example.

FIG. 9 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a one-dimensional vector according toan example.

FIG. 10 is a diagram illustrating wide-angle intra prediction modesaccording to an embodiment of the present disclosure.

FIG. 11 is a diagram illustrating a block shape to which LFNST isapplied.

FIG. 12 is a diagram illustrating an arrangement of output data of aforward LFNST according to an example.

FIG. 13 is a diagram illustrating zero-out in a block to which 4×4 LFNSTis applied according to an example.

FIG. 14 is a diagram illustrating zero-out in a block to which 8×8 LFNSTis applied according to an example.

FIG. 15 is a flowchart illustrating an operation of a video decodingapparatus according to an embodiment of the present disclosure.

FIG. 16 is a flowchart illustrating an operation of a video encodingapparatus according to an embodiment of the present disclosure.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

While the present disclosure may be susceptible to various modificationsand include various embodiments, specific embodiments thereof have beenshown in the drawings by way of example and will now be described indetail. However, this is not intended to limit the present disclosure tothe specific embodiments disclosed herein. The terminology used hereinis for the purpose of describing specific embodiments only, and is notintended to limit technical idea of the present disclosure. The singularforms may include the plural forms unless the context clearly indicatesotherwise. The terms such as “include” and “have” are intended toindicate that features, numbers, steps, operations, elements,components, or combinations thereof used in the following descriptionexist, and thus should not be understood as that the possibility ofexistence or addition of one or more different features, numbers, steps,operations, elements, components, or combinations thereof is excluded inadvance.

Meanwhile, each component on the drawings described herein isillustrated independently for convenience of description as tocharacteristic functions different from each other, and however, it isnot meant that each component is realized by a separate hardware orsoftware. For example, any two or more of these components may becombined to form a single component, and any single component may bedivided into plural components. The embodiments in which components arecombined and/or divided will belong to the scope of the patent right ofthe present disclosure as long as they do not depart from the essence ofthe present disclosure.

Hereinafter, preferred embodiments of the present disclosure will beexplained in more detail while referring to the attached drawings. Inaddition, the same reference signs are used for the same components onthe drawings, and repeated descriptions for the same components will beomitted.

This document relates to video/image coding. For example, themethod/example disclosed in this document may relate to a VVC (VersatileVideo Coding) standard (ITU-T Rec. H.266), a next-generation video/imagecoding standard after VVC, or other video coding related standards(e.g., HEVC (High Efficiency Video Coding) standard (ITU-T Rec. H.265),EVC (essential video coding) standard, AVS2 standard, etc.).

In this document, a variety of embodiments relating to video/imagecoding may be provided, and, unless specified to the contrary, theembodiments may be combined to each other and be performed.

In this document, a video may mean a set of a series of images overtime. Generally a picture means a unit representing an image at aspecific time zone, and a slice/tile is a unit constituting a part ofthe picture. The slice/tile may include one or more coding tree units(CTUs). One picture may be constituted by one or more slices/tiles. Onepicture may be constituted by one or more tile groups. One tile groupmay include one or more tiles.

A pixel or a pel may mean a smallest unit constituting one picture (orimage). Also, ‘sample’ may be used as a term corresponding to a pixel. Asample may generally represent a pixel or a value of a pixel, and mayrepresent only a pixel/pixel value of a luma component or only apixel/pixel value of a chroma component. Alternatively, the sample mayrefer to a pixel value in the spatial domain, or when this pixel valueis converted to the frequency domain, it may refer to a transformcoefficient in the frequency domain.

A unit may represent the basic unit of image processing. The unit mayinclude at least one of a specific region and information related to theregion. One unit may include one luma block and two chroma (e.g., cb,cr) blocks. The unit and a term such as a block, an area, or the likemay be used in place of each other according to circumstances. In ageneral case, an M×N block may include a set (or an array) of samples(or sample arrays) or transform coefficients consisting of M columns andN rows.

In this document, the term “/” and “,” should be interpreted to indicate“and/or.” For instance, the expression “A/B” may mean “A and/or B.”Further, “A, B” may mean “A and/or B.” Further, “A/B/C” may mean “atleast one of A, B, and/or C.” Also, “A/B/C” may mean “at least one of A,B, and/or C.”

Further, in the document, the term “or” should be interpreted toindicate “and/or.” For instance, the expression “A or B” may include 1)only A, 2) only B, and/or 3) both A and B. In other words, the term “or”in this document should be interpreted to indicate “additionally oralternatively.”

In the present disclosure, “at least one of A and B” may mean “only A”,“only B”, or “both A and B”. In addition, in the present disclosure, theexpression “at least one of A or B” or “at least one of A and/or B” maybe interpreted as “at least one of A and B”.

In addition, in the present disclosure, “at least one of A, B, and C”may mean “only A”, “only B”, “only C”, or “any combination of A, B, andC”. In addition, “at least one of A, B, or C” or “at least one of A, B,and/or C” may mean “at least one of A, B, and C”.

In addition, a parenthesis used in the present disclosure may mean “forexample”. Specifically, when indicated as “prediction (intraprediction)”, it may mean that “intra prediction” is proposed as anexample of “prediction”. In other words, the “prediction” of the presentdisclosure is not limited to “intra prediction”, and “intra prediction”may be proposed as an example of “prediction”. In addition, whenindicated as “prediction (i.e., intra prediction)”, it may also meanthat “intra prediction” is proposed as an example of “prediction”.

Technical features individually described in one figure in the presentdisclosure may be individually implemented or may be simultaneouslyimplemented.

FIG. 1 schematically illustrates an example of a video/image codingsystem to which the present disclosure is applicable.

Referring to FIG. 1 , the video/image coding system may include a firstdevice (source device) and a second device (receive device). The sourcedevice may deliver encoded video/image information or data in the formof a file or streaming to the receive device via a digital storagemedium or network.

The source device may include a video source, an encoding apparatus, anda transmitter. The receive device may include a receiver, a decodingapparatus, and a renderer. The encoding apparatus may be called avideo/image encoding apparatus, and the decoding apparatus may be calleda video/image decoding apparatus. The transmitter may be included in theencoding apparatus. The receiver may be included in the decodingapparatus. The renderer may include a display, and the display may beconfigured as a separate device or an external component.

The video source may obtain a video/image through a process ofcapturing, synthesizing, or generating a video/image. The video sourcemay include a video/image capture device and/or a video/image generatingdevice. The video/image capture device may include, for example, one ormore cameras, video/image archives including previously capturedvideo/images, or the like. The video/image generating device mayinclude, for example, a computer, a tablet and a smartphone, and may(electronically) generate a video/image. For example, a virtualvideo/image may be generated through a computer or the like. In thiscase, the video/image capturing process may be replaced by a process ofgenerating related data.

The encoding apparatus may encode an input video/image. The encodingapparatus may perform a series of procedures such as prediction,transform, and quantization for compression and coding efficiency. Theencoded data (encoded video/image information) may be output in the formof a bitstream.

The transmitter may transmit the encoded video/image information or dataoutput in the form of a bitstream to the receiver of the receive devicethrough a digital storage medium or a network in the form of a file orstreaming. The digital storage medium may include various storagemediums such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, and the like. Thetransmitter may include an element for generating a media file through apredetermined file format, and may include an element for transmissionthrough a broadcast/communication network. The receiver mayreceive/extract the bitstream and transmit the received/extractedbitstream to the decoding apparatus.

The decoding apparatus may decode a video/image by performing a seriesof procedures such as dequantization, inverse transform, prediction, andthe like corresponding to the operation of the encoding apparatus.

The renderer may render the decoded video/image. The renderedvideo/image may be displayed through the display.

FIG. 2 is a diagram schematically illustrating a configuration of avideo/image encoding apparatus to which the present disclosure isapplicable. Hereinafter, what is referred to as the video encodingapparatus may include an image encoding apparatus.

Referring to FIG. 2 , the encoding apparatus 200 may include an imagepartitioner 210, a predictor 220, a residual processor 230, an entropyencoder 240, an adder 250, a filter 260, and a memory 270. The predictor220 may include an inter predictor 221 and an intra predictor 222. Theresidual processor 230 may include a transformer 232, a quantizer 233, adequantizer 234, an inverse transformer 235. The residual processor 230may further include a subtractor 231. The adder 250 may be called areconstructor or reconstructed block generator. The image partitioner210, the predictor 220, the residual processor 230, the entropy encoder240, the adder 250, and the filter 260, which have been described above,may be constituted by one or more hardware components (e.g., encoderchipsets or processors) according to an embodiment. Further, the memory270 may include a decoded picture buffer (DPB), and may be constitutedby a digital storage medium. The hardware component may further includethe memory 270 as an internal/external component.

The image partitioner 210 may partition an input image (or a picture ora frame) input to the encoding apparatus 200 into one or more processingunits. As one example, the processing unit may be called a coding unit(CU). In this case, starting with a coding tree unit (CTU) or thelargest coding unit (LCU), the coding unit may be recursivelypartitioned according to the Quad-tree binary-tree ternary-tree (QTBTTT)structure. For example, one coding unit may be divided into a pluralityof coding units of a deeper depth based on the quad-tree structure, thebinary-tree structure, and/or the ternary structure. In this case, forexample, the quad-tree structure may be applied first and thebinary-tree structure and/or the ternary structure may be applied later.Alternatively, the binary-tree structure may be applied first. Thecoding procedure according to the present disclosure may be performedbased on the final coding unit which is not further partitioned. In thiscase, the maximum coding unit may be used directly as a final codingunit based on coding efficiency according to the image characteristic.Alternatively, the coding unit may be recursively partitioned intocoding units of a further deeper depth as needed, so that the codingunit of an optimal size may be used as a final coding unit. Here, thecoding procedure may include procedures such as prediction, transform,and reconstruction, which will be described later. As another example,the processing unit may further include a prediction unit (PU) or atransform unit (TU). In this case, the prediction unit and the transformunit may be split or partitioned from the above-described final codingunit. The prediction unit may be a unit of sample prediction, and thetransform unit may be a unit for deriving a transform coefficient and/ora unit for deriving a residual signal from a transform coefficient.

The unit and a term such as a block, an area, or the like may be used inplace of each other according to circumstances. In a general case, anM×N block may represent a set of samples or transform coefficientsconsisting of M columns and N rows. The sample may generally represent apixel or a value of a pixel, and may represent only a pixel/pixel valueof a luma component, or only a pixel/pixel value of a chroma component.The sample may be used as a term corresponding to a pixel or a pel ofone picture (or image).

The subtractor 231 subtractes a prediction signal (predicted block,prediction sample array) output from the predictor 220 from an inputimage signal (original block, original sample array) to generate aresidual signal (residual block, residual sample array), and thegenerated residual signal is transmitted to the transformer 232. Thepredictor 220 may perform prediction on a processing target block(hereinafter, referred to as ‘current block’), and may generate apredicted block including prediction samples for the current block. Thepredictor 220 may determine whether intra prediction or inter predictionis applied on a current block or CU basis. As discussed later in thedescription of each prediction mode, the predictor may generate variousinformation relating to prediction, such as prediction mode information,and transmit the generated information to the entropy encoder 240. Theinformation on the prediction may be encoded in the entropy encoder 240and output in the form of a bitstream.

The intra predictor 222 may predict the current block by referring tosamples in the current picture. The referred samples may be located inthe neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The non-directional modes may include, for example, a DC mode and aplanar mode. The directional mode may include, for example, 33directional prediction modes or 65 directional prediction modesaccording to the degree of detail of the prediction direction. However,this is merely an example, and more or less directional prediction modesmay be used depending on a setting. The intra predictor 222 maydetermine the prediction mode applied to the current block by using theprediction mode applied to the neighboring block.

The inter predictor 221 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. The referencepicture including the reference block and the reference pictureincluding the temporal neighboring block may be same to each other ordifferent from each other. The temporal neighboring block may be calleda collocated reference block, a collocated CU (colCU), and the like, andthe reference picture including the temporal neighboring block may becalled a collocated picture (colPic). For example, the inter predictor221 may configure a motion information candidate list based onneighboring blocks and generate information indicating which candidateis used to derive a motion vector and/or a reference picture index ofthe current block. Inter prediction may be performed based on variousprediction modes. For example, in the case of a skip mode and a mergemode, the inter predictor 221 may use motion information of theneighboring block as motion information of the current block. In theskip mode, unlike the merge mode, the residual signal may not betransmitted. In the case of the motion information prediction (motionvector prediction, MVP) mode, the motion vector of the neighboring blockmay be used as a motion vector predictor and the motion vector of thecurrent block may be indicated by signaling a motion vector difference.

The predictor 220 may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Further,the predictor may be based on an intra block copy (IBC) prediction mode,or a palette mode in order to perform prediction on a block. The IBCprediction mode or palette mode may be used for content image/videocoding of a game or the like, such as screen content coding (SCC).Although the IBC basically performs prediction in a current block, itcan be performed similarly to inter prediction in that it derives areference block in a current block. That is, the IBC may use at leastone of inter prediction techniques described in the present disclosure.

The prediction signal generated through the inter predictor 221 and/orthe intra predictor 222 may be used to generate a reconstructed signalor to generate a residual signal. The transformer 232 may generatetransform coefficients by applying a transform technique to the residualsignal. For example, the transform technique may include at least one ofa discrete cosine transform (DCT), a discrete sine transform (DST), aKarhunen-Loève transform (KLT), a graph-based transform (GBT), or aconditionally non-linear transform (CNT). Here, the GBT means transformobtained from a graph when relationship information between pixels isrepresented by the graph. The CNT refers to transform obtained based ona prediction signal generated using all previously reconstructed pixels.In addition, the transform process may be applied to square pixel blockshaving the same size or may be applied to blocks having a variable sizerather than the square one.

The quantizer 233 may quantize the transform coefficients and transmitthem to the entropy encoder 240, and the entropy encoder 240 may encodethe quantized signal (information on the quantized transformcoefficients) and output the encoded signal in a bitstream. Theinformation on the quantized transform coefficients may be referred toas residual information. The quantizer 233 may rearrange block typequantized transform coefficients into a one-dimensional vector formbased on a coefficient scan order, and generate information on thequantized transform coefficients based on the quantized transformcoefficients of the one-dimensional vector form. The entropy encoder 240may perform various encoding methods such as, for example, exponentialGolomb, context-adaptive variable length coding (CAVLC),context-adaptive binary arithmetic coding (CABAC), and the like. Theentropy encoder 240 may encode information necessary for video/imagereconstruction other than quantized transform coefficients (e.g. valuesof syntax elements, etc.) together or separately. Encoded information(e.g., encoded video/image information) may be transmitted or stored ona unit basis of a network abstraction layer (NAL) in the form of abitstream. The video/image information may further include informationon various parameter sets such as an adaptation parameter set (APS), apicture parameter set (PPS), a sequence parameter set (SPS), a videoparameter set (VPS) or the like. Further, the video/image informationmay further include general constraint information. In the presentdisclosure, information and/or syntax elements which aretransmitted/signaled to the decoding apparatus from the encodingapparatus may be included in video/image information. The video/imageinformation may be encoded through the above-described encodingprocedure and included in the bitstream. The bitstream may betransmitted through a network, or stored in a digital storage medium.Here, the network may include a broadcast network, a communicationnetwork and/or the like, and the digital storage medium may includevarious storage media such as USB, SD, CD, DVD, Blu-ray, HDD, SSD, andthe like. A transmitter (not shown) which transmits a signal output fromthe entropy encoder 240 and/or a storage (not shown) which stores it maybe configured as an internal/external element of the encoding apparatus200, or the transmitter may be included in the entropy encoder 240.

Quantized transform coefficients output from the quantizer 233 may beused to generate a prediction signal. For example, by applyingdequantization and inverse transform to quantized transform coefficientsthrough the dequantizer 234 and the inverse transformer 235, theresidual signal (residual block or residual samples) may bereconstructed. The adder 155 adds the reconstructed residual signal to aprediction signal output from the inter predictor 221 or the intrapredictor 222, so that a reconstructed signal (reconstructed picture,reconstructed block, reconstructed sample array) may be generated. Whenthere is no residual for a processing target block as in a case wherethe skip mode is applied, the predicted block may be used as areconstructed block. The adder 250 may be called a reconstructor or areconstructed block generator. The generated reconstructed signal may beused for intra prediction of a next processing target block in thecurrent block, and as described later, may be used for inter predictionof a next picture through filtering.

Meanwhile, in the picture encoding and/or reconstructing process, lumamapping with chroma scaling (LMCS) may be applied.

The filter 260 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 260 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may storethe modified reconstructed picture in the memory 270, specifically inthe DPB of the memory 270. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like. As discussed later in thedescription of each filtering method, the filter 260 may generatevarious information relating to filtering, and transmit the generatedinformation to the entropy encoder 240. The information on the filteringmay be encoded in the entropy encoder 240 and output in the form of abitstream.

The modified reconstructed picture which has been transmitted to thememory 270 may be used as a reference picture in the inter predictor221. Through this, the encoding apparatus can avoid prediction mismatchin the encoding apparatus 100 and a decoding apparatus when the interprediction is applied, and can also improve coding efficiency.

The memory 270 DPB may store the modified reconstructed picture in orderto use it as a reference picture in the inter predictor 221. The memory270 may store motion information of a block in the current picture, fromwhich motion information has been derived (or encoded) and/or motioninformation of blocks in an already reconstructed picture. The storedmotion information may be transmitted to the inter predictor 221 to beutilized as motion information of a neighboring block or motioninformation of a temporal neighboring block. The memory 270 may storereconstructed samples of reconstructed blocks in the current picture,and transmit them to the intra predictor 222.

FIG. 3 is a diagram schematically illustrating a configuration of avideo/image decoding apparatus to which the present disclosure isapplicable.

Referring to FIG. 3 , the video decoding apparatus 300 may include anentropy decoder 310, a residual processor 320, a predictor 330, an adder340, a filter 350 and a memory 360. The predictor 330 may include aninter predictor 331 and an intra predictor 332. The residual processor320 may include a dequantizer 321 and an inverse transformer 321. Theentropy decoder 310, the residual processor 320, the predictor 330, theadder 340, and the filter 350, which have been described above, may beconstituted by one or more hardware components (e.g., decoder chipsetsor processors) according to an embodiment. Further, the memory 360 mayinclude a decoded picture buffer (DPB), and may be constituted by adigital storage medium. The hardware component may further include thememory 360 as an internal/external component.

When a bitstream including video/image information is input, thedecoding apparatus 300 may reconstruct an image correspondingly to aprocess by which video/image information has been processed in theencoding apparatus of FIG. 2 . For example, the decoding apparatus 300may derive units/blocks based on information relating to block partitionobtained from the bitstream. The decoding apparatus 300 may performdecoding by using a processing unit applied in the encoding apparatus.Therefore, the processing unit of decoding may be, for example, a codingunit, which may be partitioned along the quad-tree structure, thebinary-tree structure, and/or the ternary-tree structure from a codingtree unit or a largest coding unit. One or more transform units may bederived from the coding unit. And, the reconstructed image signaldecoded and output through the decoding apparatus 300 may be reproducedthrough a reproducer.

The decoding apparatus 300 may receive a signal output from the encodingapparatus of FIG. 2 in the form of a bitstream, and the received signalmay be decoded through the entropy decoder 310. For example, the entropydecoder 310 may parse the bitstream to derive information (e.g.,video/image information) required for image reconstruction (or picturereconstruction). The video/image information may further includeinformation on various parameter sets such as an adaptation parameterset (APS), a picture parameter set (PPS), a sequence parameter set(SPS), a video parameter set (VPS) or the like. Further, the video/imageinformation may further include general constraint information. Thedecoding apparatus may decode a picture further based on information onthe parameter set and/or the general constraint information. In thepresent disclosure, signaled/received information and/or syntaxelements, which will be described later, may be decoded through thedecoding procedure and be obtained from the bitstream. For example, theentropy decoder 310 may decode information in the bitstream based on acoding method such as exponential Golomb encoding, CAVLC, CABAC, or thelike, and may output a value of a syntax element necessary for imagereconstruction and quantized values of a transform coefficient regardinga residual. More specifically, a CABAC entropy decoding method mayreceive a bin corresponding to each syntax element in a bitstream,determine a context model using decoding target syntax elementinformation and decoding information of neighboring and decoding targetblocks, or information of symbol/bin decoded in a previous step, predictbin generation probability according to the determined context model andperform arithmetic decoding of the bin to generate a symbolcorresponding to each syntax element value. Here, the CABAC entropydecoding method may update the context model using information of asymbol/bin decoded for a context model of the next symbol/bin afterdetermination of the context model. Information on prediction amonginformation decoded in the entropy decoder 310 may be provided to thepredictor (inter predictor 332 and intra predictor 331), and residualvalues, that is, quantized transform coefficients, on which entropydecoding has been performed in the entropy decoder 310, and associatedparameter information may be input to the residual processor 320. Theresidual processor 320 may derive a residual signal (residual block,residual samples, residual sample array). Further, information onfiltering among information decoded in the entropy decoder 310 may beprovided to the filter 350. Meanwhile, a receiver (not shown) whichreceives a signal output from the encoding apparatus may furtherconstitute the decoding apparatus 300 as an internal/external element,and the receiver may be a component of the entropy decoder 310.Meanwhile, the decoding apparatus according to the present disclosuremay be called a video/image/picture coding apparatus, and the decodingapparatus may be classified into an information decoder(video/image/picture information decoder) and a sample decoder(video/image/picture sample decoder). The information decoder mayinclude the entropy decoder 310, and the sample decoder may include atleast one of the dequantizer 321, the inverse transformer 322, the adder340, the filter 350, the memory 360, the inter predictor 332, and theintra predictor 331.

The dequantizer 321 may output transform coefficients by dequantizingthe quantized transform coefficients. The dequantizer 321 may rearrangethe quantized transform coefficients in the form of a two-dimensionalblock. In this case, the rearrangement may perform rearrangement basedon an order of coefficient scanning which has been performed in theencoding apparatus. The dequantizer 321 may perform dequantization onthe quantized transform coefficients using quantization parameter (e.g.,quantization step size information), and obtain transform coefficients.

The deqauntizer 322 obtains a residual signal (residual block, residualsample array) by inverse transforming transform coefficients.

The predictor may perform prediction on the current block, and generatea predicted block including prediction samples for the current block.The predictor may determine whether intra prediction or inter predictionis applied to the current block based on the information on predictionoutput from the entropy decoder 310, and specifically may determine anintra/inter prediction mode.

The predictor may generate a prediction signal based on variousprediction methods. For example, the predictor may apply intraprediction or inter prediction for prediction on one block, and, aswell, may apply intra prediction and inter prediction at the same time.This may be called combined inter and intra prediction (CIIP). Inaddition, the predictor may perform intra block copy (IBC) forprediction on a block. The intra block copy may be used for contentimage/video coding of a game or the like, such as screen content coding(SCC). Although the IBC basically performs prediction in a currentblock, it can be performed similarly to inter prediction in that itderives a reference block in a current block. That is, the IBC may useat least one of inter prediction techniques described in the presentdisclosure.

The intra predictor 331 may predict the current block by referring tothe samples in the current picture. The referred samples may be locatedin the neighbor of or apart from the current block according to theprediction mode. In the intra prediction, prediction modes may include aplurality of non-directional modes and a plurality of directional modes.The intra predictor 331 may determine the prediction mode applied to thecurrent block by using the prediction mode applied to the neighboringblock.

The inter predictor 332 may derive a predicted block for the currentblock based on a reference block (reference sample array) specified by amotion vector on a reference picture. At this time, in order to reducethe amount of motion information transmitted in the inter predictionmode, the motion information may be predicted on a block, subblock, orsample basis based on correlation of motion information between theneighboring block and the current block. The motion information mayinclude a motion vector and a reference picture index. The motioninformation may further include inter prediction direction (L0prediction, L1 prediction, Bi prediction, etc.) information. In the caseof inter prediction, the neighboring block may include a spatialneighboring block existing in the current picture and a temporalneighboring block existing in the reference picture. For example, theinter predictor 332 may configure a motion information candidate listbased on neighboring blocks, and derive a motion vector and/or areference picture index of the current block based on received candidateselection information. Inter prediction may be performed based onvarious prediction modes, and the information on prediction may includeinformation indicating a mode of inter prediction for the current block.

The adder 340 may generate a reconstructed signal (reconstructedpicture, reconstructed block, reconstructed sample array) by adding theobtained residual signal to the prediction signal (predicted block,prediction sample array) output from the predictor 330. When there is noresidual for a processing target block as in a case where the skip modeis applied, the predicted block may be used as a reconstructed block.

The adder 340 may be called a reconstructor or a reconstructed blockgenerator. The generated reconstructed signal may be used for intraprediction of a next processing target block in the current block, andas described later, may be output through filtering or be used for interprediction of a next picture.

Meanwhile, in the picture decoding process, luma mapping with chromascaling (LMCS) may be applied.

The filter 350 may improve subjective/objective video quality byapplying the filtering to the reconstructed signal. For example, thefilter 350 may generate a modified reconstructed picture by applyingvarious filtering methods to the reconstructed picture, and may transmitthe modified reconstructed picture in the memory 360, specifically inthe DPB of the memory 360. The various filtering methods may include,for example, deblocking filtering, sample adaptive offset, an adaptiveloop filter, a bilateral filter or the like.

The (modified) reconstructed picture which has been stored in the DPB ofthe memory 360 may be used as a reference picture in the inter predictor332. The memory 360 may store motion information of a block in thecurrent picture, from which motion information has been derived (ordecoded) and/or motion information of blocks in an already reconstructedpicture. The stored motion information may be transmitted to the interpredictor 260 to be utilized as motion information of a neighboringblock or motion information of a temporal neighboring block. The memory360 may store reconstructed samples of reconstructed blocks in thecurrent picture, and transmit them to the intra predictor 331.

In this specification, the examples described in the predictor 330, thedequantizer 321, the inverse transformer 322, and the filter 350 of thedecoding apparatus 300 may be similarly or correspondingly applied tothe predictor 220, the dequantizer 234, the inverse transformer 235, andthe filter 260 of the encoding apparatus 200, respectively.

As described above, prediction is performed in order to increasecompression efficiency in performing video coding. Through this, apredicted block including prediction samples for a current block, whichis a coding target block, may be generated. Here, the predicted blockincludes prediction samples in a space domain (or pixel domain). Thepredicted block may be indentically derived in the encoding apparatusand the decoding apparatus, and the encoding apparatus may increaseimage coding efficiency by signaling to the decoding apparatus notoriginal sample value of an original block itself but information onresidual (residual information) between the original block and thepredicted block. The decoding apparatus may derive a residual blockincluding residual samples based on the residual information, generate areconstructed block including reconstructed samples by adding theresidual block to the predicted block, and generate a reconstructedpicture including reconstructed blocks.

The residual information may be generated through transform andquantization procedures. For example, the encoding apparatus may derivea residual block between the original block and the predicted block,derive transform coefficients by performing a transform procedure onresidual samples (residual sample array) included in the residual block,and derive quantized transform coefficients by performing a quantizationprocedure on the transform coefficients, so that it may signalassociated residual information to the decoding apparatus (through abitstream). Here, the residual information may include valueinformation, position information, a transform technique, transformkernel, a quantization parameter or the like of the quantized transformcoefficients. The decoding apparatus may perform aquantization/dequantization procedure and derive the residual samples(or residual sample block), based on residual information. The decodingapparatus may generate a reconstructed block based on a predicted blockand the residual block. The encoding apparatus may derive a residualblock by dequantizing/inverse transforming quantized transformcoefficients for reference for inter prediction of a next picture, andmay generate a reconstructed picture based on this.

FIG. 4 illustrates the structure of a content streaming system to whichthe present disclosure is applied.

Further, the contents streaming system to which the present disclosureis applied may largely include an encoding server, a streaming server, aweb server, a media storage, a user equipment, and a multimedia inputdevice.

The encoding server functions to compress to digital data the contentsinput from the multimedia input devices, such as the smart phone, thecamera, the camcoder and the like, to generate a bitstream, and totransmit it to the streaming server. As another example, in a case wherethe multimedia input device, such as, the smart phone, the camera, thecamcoder or the like, directly generates a bitstream, the encodingserver may be omitted. The bitstream may be generated by an encodingmethod or a bitstream generation method to which the present disclosureis applied. And the streaming server may store the bitstream temporarilyduring a process to transmit or receive the bitstream.

The streaming server transmits multimedia data to the user equipment onthe basis of a user's request through the web server, which functions asan instrument that informs a user of what service there is. When theuser requests a service which the user wants, the web server transfersthe request to the streaming server, and the streaming server transmitsmultimedia data to the user. In this regard, the contents streamingsystem may include a separate control server, and in this case, thecontrol server functions to control commands/responses betweenrespective equipments in the content streaming system.

The streaming server may receive contents from the media storage and/orthe encoding server. For example, in a case the contents are receivedfrom the encoding server, the contents may be received in real time. Inthis case, the streaming server may store the bitstream for apredetermined period of time to provide the streaming service smoothly.

For example, the user equipment may include a mobile phone, a smartphone, a laptop computer, a digital broadcasting terminal, a personaldigital assistant (PDA), a portable multimedia player (PMP), anavigation, a slate PC, a tablet PC, an ultrabook, a wearable device(e.g., a watch-type terminal (smart watch), a glass-type terminal (smartglass), a head mounted display (HMD)), a digital TV, a desktop computer,a digital signage or the like. Each of servers in the contents streamingsystem may be operated as a distributed server, and in this case, datareceived by each server may be processed in distributed manner.

FIG. 5 schematically illustrates a multiple transform techniqueaccording to an embodiment of the present disclosure.

Referring to FIG. 5 , a transformer may correspond to the transformer inthe encoding apparatus of foregoing FIG. 2 , and an inverse transformermay correspond to the inverse transformer in the encoding apparatus offoregoing FIG. 2 , or to the inverse transformer in the decodingapparatus of FIG. 3 .

The transformer may derive (primary) transform coefficients byperforming a primary transform based on residual samples (residualsample array) in a residual block (S510). This primary transform may bereferred to as a core transform. Herein, the primary transform may bebased on multiple transform selection (MTS), and when a multipletransform is applied as the primary transform, it may be referred to asa multiple core transform.

The multiple core transform may represent a method of transformingadditionally using discrete cosine transform (DCT) type 2 and discretesine transform (DST) type 7, DCT type 8, and/or DST type 1. That is, themultiple core transform may represent a transform method of transforminga residual signal (or residual block) of a space domain into transformcoefficients (or primary transform coefficients) of a frequency domainbased on a plurality of transform kernels selected from among the DCTtype 2, the DST type 7, the DCT type 8 and the DST type 1. Herein, theprimary transform coefficients may be called temporary transformcoefficients from the viewpoint of the transformer.

In other words, when the conventional transform method is applied,transform coefficients might be generated by applying transform from aspace domain to a frequency domain for a residual signal (or residualblock) based on the DCT type 2. Unlike to this, when the multiple coretransform is applied, transform coefficients (or primary transformcoefficients) may be generated by applying transform from a space domainto a frequency domain for a residual signal (or residual block) based onthe DCT type 2, the DST type 7, the DCT type 8, and/or DST type 1.Herein, the DCT type 2, the DST type 7, the DCT type 8, and the DST type1 may be called a transform type, transform kernel or transform core.These DCT/DST transform types can be defined based on basis functions.

When the multiple core transform is performed, a vertical transformkernel and a horizontal transform kernel for a target block may beselected from among the transform kernels, a vertical transform may beperformed on the target block based on the vertical transform kernel,and a horizontal transform may be performed on the target block based onthe horizontal transform kernel. Here, the horizontal transform mayindicate a transform on horizontal components of the target block, andthe vertical transform may indicate a transform on vertical componentsof the target block. The vertical transform kernel/horizontal transformkernel may be adaptively determined based on a prediction mode and/or atransform index for the target block (CU or subblock) including aresidual block.

Further, according to an example, if the primary transform is performedby applying the MTS, a mapping relationship for transform kernels may beset by setting specific basis functions to predetermined values andcombining basis functions to be applied in the vertical transform or thehorizontal transform. For example, when the horizontal transform kernelis expressed as trTypeHor and the vertical direction transform kernel isexpressed as trTypeVer, a trTypeHor or trTypeVer value of 0 may be setto DCT2, a trTypeHor or trTypeVer value of 1 may be set to DST7, and atrTypeHor or trTypeVer value of 2 may be set to DCT8.

In this case, MTS index information may be encoded and signaled to thedecoding apparatus to indicate any one of a plurality of transformkernel sets. For example, an MTS index of 0 may indicate that bothtrTypeHor and trTypeVer values are 0, an MTS index of 1 may indicatethat both trTypeHor and trTypeVer values are 1, an MTS index of 2 mayindicate that the trTypeHor value is 2 and the trTypeVer value. Is 1, anMTS index of 3 may indicate that the trTypeHor value is 1 and thetrTypeVer value is 2, and an MTS index of 4 may indicate that bothtrTypeHor and trTypeVer values are 2.

In one example, transform kernel sets according to MTS index informationare illustrated in the following table.

TABLE 1 tu_mts_idx[ x0 ][ y0 ] 0 1 2 3 4 trTypeHor 0 1 2 1 2 trTypeVer 01 1 2 2

The transformer may perform a secondary transform based on the (primary)transform coefficients to derive modified (secondary) transformcoefficients (S520). The primary transform is a transform from a spatialdomain to a frequency domain, and the secondary transform refers totransforming into a more compact expression using a correlation existingbetween (primary) transform coefficients. The secondary transform mayinclude a non-separable transform. In this case, the secondary transformmay be referred to as a non-separable secondary transform (NSST) or amode-dependent non-separable secondary transform (MDNSST). The NSST mayrepresent a transform that secondarily transforms (primary) transformcoefficients derived through the primary transform based on anon-separable transform matrix to generate modified transformcoefficients (or secondary transform coefficients) for a residualsignal. Here, the transform may be applied at once without separating(or independently applying a horizontal/vertical transform) a verticaltransform and a horizontal transform to the (primary) transformcoefficients based on the non-separable transform matrix. In otherwords, the NSST is not separately applied to the (primary) transformcoefficients in a vertical direction and a horizontal direction, and mayrepresent, for example, a transform method of rearrangingtwo-dimensional signals (transform coefficients) into a one-dimensionalsignal through a specific predetermined direction (e.g., row-firstdirection or column-first direction) and then generating modifiedtransform coefficients (or secondary transform coefficients) based onthe non-separable transform matrix. For example, a row-first order is todispose in a line in order of a 1st row, a 2nd row, . . . , an Nth rowfor M×N blocks, and a column-first order is to dispose in a line inorder of a 1st column, a 2nd column, . . . , an Mth column for M×Nblocks. The NSST may be applied to a top-left region of a block(hereinafter, referred to as a transform coefficient block) configuredwith (primary) transform coefficients. For example, when both a width Wand height H of the transform coefficient block are 8 or more, an 8×8NSST may be applied to the top-left 8×8 region of the transformcoefficient block. Further, while both the width (W) and height (H) ofthe transform coefficient block are 4 or more, when the width (W) orheight (H) of the transform coefficient block is smaller than 8, 4×4NSST may be applied to the top-left min(8·W)×min(8,H) region of thetransform coefficient block. However, the embodiment is not limitedthereto, and for example, even if only the condition that the width W orthe height H of the transform coefficient block is 4 or greater issatisfied, the 4×4 NSST may be applied to the top-left endmin(8,W)×min(8,H) region of the transform coefficient block.

Specifically, for example, if a 4×4 input block is used, thenon-separable secondary transform may be performed as follows.

The 4×4 input block X may be represented as follows.

$\begin{matrix}{X = \begin{bmatrix}X_{00} & X_{01} & X_{02} & X_{03} \\X_{10} & X_{11} & X_{12} & X_{13} \\X_{20} & X_{21} & X_{22} & X_{23} \\X_{30} & X_{31} & X_{32} & X_{33}\end{bmatrix}} & \left\lbrack {{Equation}1} \right\rbrack\end{matrix}$

If the X is represented in the form of a vector, the vector

may be represented as below.

=[X ₀₀ X ₀₁ X ₀₂ X ₀₃ X ₁₀ X ₁₁ X ₁₂ X ₁₃ X ₂₀ X ₂₁ X ₂₂ X ₂₃ X ₃₀ X ₃₁X ₃₂ X ₃₃]^(T)  [Equation 2]

In Equation 2, the vector

is a one-dimensional vector obtained by rearranging the two-dimensionalblock X of Equation 1 according to the row-first order.

In this case, the secondary non-separable transform may be calculated asbelow.

=T·

  [Equation 3]

In this equation,

represents a transform coefficient vector, and T represents a 16×16(non-separable) transform matrix.

Through foregoing Equation 3, a 16×1 transform coefficient vector

may be derived, and the

may be re-organized into a 4×4 block through a scan order (horizontal,vertical, diagonal and the like). However, the above-describedcalculation is an example, and hypercube-Givens transform (HyGT) or thelike may be used for the calculation of the non-separable secondarytransform in order to reduce the computational complexity of thenon-separable secondary transform.

Meanwhile, in the non-separable secondary transform, a transform kernel(or transform core, transform type) may be selected to be modedependent. In this case, the mode may include the intra prediction modeand/or the inter prediction mode.

As described above, the non-separable secondary transform may beperformed based on an 8×8 transform or a 4×4 transform determined basedon the width (W) and the height (H) of the transform coefficient block.The 8×8 transform refers to a transform that is applicable to an 8×8region included in the transform coefficient block when both W and H areequal to or greater than 8, and the 8×8 region may be a top-left 8×8region in the transform coefficient block. Similarly, the 4×4 transformrefers to a transform that is applicable to a 4×4 region included in thetransform coefficient block when both W and H are equal to or greaterthan 4, and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block. For example, an 8×8 transform kernel matrix may be a64×64/16×64 matrix, and a 4×4 transform kernel matrix may be a16×16/8×16 matrix.

Here, to select a mode-dependent transform kernel, two non-separablesecondary transform kernels per transform set for a non-separablesecondary transform may be configured for both the 8×8 transform and the4×4 transform, and there may be four transform sets. That is, fourtransform sets may be configured for the 8×8 transform, and fourtransform sets may be configured for the 4×4 transform. In this case,each of the four transform sets for the 8×8 transform may include two8×8 transform kernels, and each of the four transform sets for the 4×4transform may include two 4×4 transform kernels.

However, as the size of the transform, that is, the size of a region towhich the transform is applied, may be, for example, a size other than8×8 or 4×4, the number of sets may be n, and the number of transformkernels in each set may be k.

The transform set may be referred to as an NSST set or an LFNST set. Aspecific set among the transform sets may be selected, for example,based on the intra prediction mode of the current block (CU orsubblock). A low-frequency non-separable transform (LFNST) may be anexample of a reduced non-separable transform, which will be describedlater, and represents a non-separable transform for a low frequencycomponent.

For reference, for example, the intra prediction mode may include twonon-directional (or non-angular) intra prediction modes and 65directional (or angular) intra prediction modes. The non-directionalintra prediction modes may include a planar intra prediction mode of No.0 and a DC intra prediction mode of No. 1, and the directional intraprediction modes may include 65 intra prediction modes of Nos. 2 to 66.However, this is an example, and this document may be applied even whenthe number of intra prediction modes is different. Meanwhile, in somecases, intra prediction mode No. 67 may be further used, and the intraprediction mode No. 67 may represent a linear model (LM) mode.

FIG. 6 exemplarily shows intra directional modes of 65 predictiondirections.

Referring to FIG. 6 , on the basis of intra prediction mode 34 having aleft upward diagonal prediction direction, the intra prediction modesmay be divided into intra prediction modes having horizontaldirectionality and intra prediction modes having verticaldirectionality. In FIG. 6 , H and V denote horizontal directionality andvertical directionality, respectively, and numerals −32 to 32 indicatedisplacements in 1/32 units on a sample grid position. These numeralsmay represent an offset for a mode index value. Intra prediction modes 2to 33 have the horizontal directionality, and intra prediction modes 34to 66 have the vertical directionality. Strictly speaking, intraprediction mode 34 may be considered as being neither horizontal norvertical, but may be classified as belonging to the horizontaldirectionality in determining a transform set of a secondary transform.This is because input data is transposed to be used for a verticaldirection mode symmetrical on the basis of intra prediction mode 34, andan input data alignment method for a horizontal mode is used for intraprediction mode 34. Transposing input data means that rows and columnsof two-dimensional M×N block data are switched into N×M data. Intraprediction mode 18 and intra prediction mode 50 may represent ahorizontal intra prediction mode and a vertical intra prediction mode,respectively, and intra prediction mode 2 may be referred to as a rightupward diagonal intra prediction mode because intra prediction mode 2has a left reference pixel and performs prediction in a right upwarddirection. Likewise, intra prediction mode 34 may be referred to as aright downward diagonal intra prediction mode, and intra prediction mode66 may be referred to as a left downward diagonal intra prediction mode.

According to an example, the four transform sets according to the intraprediction mode may be mapped, for example, as shown in the followingtable.

TABLE 2 predModeIntra lfnstTrSetIdx predModeIntra < 0 1 0 <=predModeIntra <= 1 0  2 <= predModeIntra <= 12 1 13 <= predModeIntra <=23 2 24 <= predModeIntra <= 44 3 45 <= predModeIntra <= 55 2 56 <=predModeIntra <= 80 1

As shown in Table 2, any one of the four transform sets, that is,lfnstTrSetIdx, may be mapped to any one of four indexes, that is, 0 to3, according to the intra prediction mode.

When it is determined that a specific set is used for the non-separabletransform, one of k transform kernels in the specific set may beselected through a non-separable secondary transform index. An encodingapparatus may derive a non-separable secondary transform indexindicating a specific transform kernel based on a rate-distortion (RD)check and may signal the non-separable secondary transform index to adecoding apparatus. The decoding apparatus may select one of the ktransform kernels in the specific set based on the non-separablesecondary transform index. For example, lfnst index value 0 may refer toa first non-separable secondary transform kernel, lfnst index value 1may refer to a second non-separable secondary transform kernel, andlfnst index value 2 may refer to a third non-separable secondarytransform kernel. Alternatively, lfnst index value 0 may indicate thatthe first non-separable secondary transform is not applied to the targetblock, and lfnst index values 1 to 3 may indicate the three transformkernels.

The transformer may perform the non-separable secondary transform basedon the selected transform kernels, and may obtain modified (secondary)transform coefficients. As described above, the modified transformcoefficients may be derived as transform coefficients quantized throughthe quantizer, and may be encoded and signaled to the decoding apparatusand transferred to the dequantizer/inverse transformer in the encodingapparatus.

Meanwhile, as described above, if the secondary transform is omitted,(primary) transform coefficients, which are an output of the primary(separable) transform, may be derived as transform coefficientsquantized through the quantizer as described above, and may be encodedand signaled to the decoding apparatus and transferred to thedequantizer/inverse transformer in the encoding apparatus.

The inverse transformer may perform a series of procedures in theinverse order to that in which they have been performed in theabove-described transformer. The inverse transformer may receive(dequantized) transformer coefficients, and derive (primary) transformcoefficients by performing a secondary (inverse) transform (S550), andmay obtain a residual block (residual samples) by performing a primary(inverse) transform on the (primary) transform coefficients (S560). Inthis connection, the primary transform coefficients may be calledmodified transform coefficients from the viewpoint of the inversetransformer. As described above, the encoding apparatus and the decodingapparatus may generate the reconstructed block based on the residualblock and the predicted block, and may generate the reconstructedpicture based on the reconstructed block.

The decoding apparatus may further include a secondary inverse transformapplication determinator (or an element to determine whether to apply asecondary inverse transform) and a secondary inverse transformdeterminator (or an element to determine a secondary inverse transform).The secondary inverse transform application determinator may determinewhether to apply a secondary inverse transform. For example, thesecondary inverse transform may be an NSST, an RST, or an LFNST and thesecondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a secondarytransform flag obtained by parsing the bitstream. In another example,the secondary inverse transform application determinator may determinewhether to apply the secondary inverse transform based on a transformcoefficient of a residual block.

The secondary inverse transform determinator may determine a secondaryinverse transform. In this case, the secondary inverse transformdeterminator may determine the secondary inverse transform applied tothe current block based on an LFNST (NSST or RST) transform setspecified according to an intra prediction mode. In an embodiment, asecondary transform determination method may be determined depending ona primary transform determination method. Various combinations ofprimary transforms and secondary transforms may be determined accordingto the intra prediction mode. Further, in an example, the secondaryinverse transform determinator may determine a region to which asecondary inverse transform is applied based on the size of the currentblock.

Meanwhile, as described above, if the secondary (inverse) transform isomitted, (dequantized) transform coefficients may be received, theprimary (separable) inverse transform may be performed, and the residualblock (residual samples) may be obtained. As described above, theencoding apparatus and the decoding apparatus may generate thereconstructed block based on the residual block and the predicted block,and may generate the reconstructed picture based on the reconstructedblock.

Meanwhile, in the present disclosure, a reduced secondary transform(RST) in which the size of a transform matrix (kernel) is reduced may beapplied in the concept of NSST in order to reduce the amount ofcomputation and memory required for the non-separable secondarytransform.

Meanwhile, the transform kernel, the transform matrix, and thecoefficient constituting the transform kernel matrix, that is, thekernel coefficient or the matrix coefficient, described in the presentdisclosure may be expressed in 8 bits. This may be a condition forimplementation in the decoding apparatus and the encoding apparatus, andmay reduce the amount of memory required to store the transform kernelwith a performance degradation that can be reasonably accommodatedcompared to the existing 9 bits or 10 bits. In addition, the expressingof the kernel matrix in 8 bits may allow a small multiplier to be used,and may be more suitable for single instruction multiple data (SIMD)instructions used for optimal software implementation.

In the present specification, the term “RST” may mean a transform whichis performed on residual samples for a target block based on a transformmatrix whose size is reduced according to a reduced factor. In the caseof performing the reduced transform, the amount of computation requiredfor transform may be reduced due to a reduction in the size of thetransform matrix. That is, the RST may be used to address thecomputational complexity issue occurring at the non-separable transformor the transform of a block of a great size.

RST may be referred to as various terms, such as reduced transform,reduced secondary transform, reduction transform, simplified transform,simple transform, and the like, and the name which RST may be referredto as is not limited to the listed examples. Alternatively, ince the RSTis mainly performed in a low frequency region including a non-zerocoefficient in a transform block, it may be referred to as aLow-Frequency Non-Separable Transform (LFNST). The transform index maybe referred to as an LFNST index.

Meanwhile, when the secondary inverse transform is performed based onRST, the inverse transformer 235 of the encoding apparatus 200 and theinverse transformer 322 of the decoding apparatus 300 may include aninverse reduced secondary transformer which derives modified transformcoefficients based on the inverse RST of the transform coefficients, andan inverse primary transformer which derives residual samples for thetarget block based on the inverse primary transform of the modifiedtransform coefficients. The inverse primary transform refers to theinverse transform of the primary transform applied to the residual. Inthe present disclosure, deriving a transform coefficient based on atransform may refer to deriving a transform coefficient by applying thetransform.

FIG. 7 is a diagram illustrating an RST according to an embodiment ofthe present disclosure.

In the present disclosure, a “target block” may refer to a current blockto be coded, a residual block, or a transform block.

In the RST according to an example, an N-dimensional vector may bemapped to an R-dimensional vector located in another space, so that thereduced transform matrix may be determined, where R is less than N. Nmay mean the square of the length of a side of a block to which thetransform is applied, or the total number of transform coefficientscorresponding to a block to which the transform is applied, and thereduced factor may mean an R/N value. The reduced factor may be referredto as a reduced factor, reduction factor, simplified factor, simplefactor or other various terms. Meanwhile, R may be referred to as areduced coefficient, but according to circumstances, the reduced factormay mean R. Further, according to circumstances, the reduced factor maymean the N/R value.

In an example, the reduced factor or the reduced coefficient may besignaled through a bitstream, but the example is not limited to this.For example, a predefined value for the reduced factor or the reducedcoefficient may be stored in each of the encoding apparatus 200 and thedecoding apparatus 300, and in this case, the reduced factor or thereduced coefficient may not be signaled separately.

The size of the reduced transform matrix according to an example may beR×N less than N×N, the size of a conventional transform matrix, and maybe defined as in Equation 4 below.

$\begin{matrix}{T_{R \times N} = \begin{bmatrix}t_{11} & t_{12} & t_{13} & \ldots & t_{1N} \\t_{21} & t_{22} & t_{23} & & t_{2N} \\ & \vdots & & \ddots & \vdots \\t_{R1} & t_{R2} & t_{R3} & \ldots & t_{RN}\end{bmatrix}} & \left\lbrack {{Equation}4} \right\rbrack\end{matrix}$

The matrix T in the Reduced Transform block shown in (a) of FIG. 7 maymean the matrix T_(R×N) of Equation 4. As shown in (a) of FIG. 7 , whenthe reduced transform matrix T_(R×N) is multiplied to residual samplesfor the target block, transform coefficients for the target block may bederived.

In an example, if the size of the block to which the transform isapplied is 8×8 and R=16 (i.e., R/N= 16/64=¼), then the RST according to(a) of FIG. 7 may be expressed as a matrix operation as shown inEquation 5 below. In this case, memory and multiplication calculationcan be reduced to approximately ¼ by the reduced factor.

In the present disclosure, a matrix operation may be understood as anoperation of multiplying a column vector by a matrix, disposed on theleft of the column vector, to obtain a column vector.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{1,2} & t_{1,3} & & t_{1,64} \\t_{2,1} & t_{2,2} & t_{2,3} & \ldots & t_{2,64} \\ & \vdots & & \ddots & \vdots \\t_{16,1} & t_{16,2} & t_{16,3} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}r_{1} \\r_{2} \\ \vdots \\r_{64}\end{bmatrix}} & \left\lbrack {{Equation}5} \right\rbrack\end{matrix}$

In Equation 5, r1 to r64 may represent residual samples for the targetblock and may be specifically transform coefficients generated byapplying a primary transform. As a result of the calculation of Equation5 transform coefficients ci for the target block may be derived, and aprocess of deriving ci may be as in Equation 6.

$\begin{matrix}{\begin{matrix}

\end{matrix}\begin{matrix}\begin{matrix}{{for}i{from}{to}R:{}} \\{{ci} = {0}} \\{{for}j{from}1{to}N} \\{{ci} + {{tij}*{rj}}}\end{matrix}\end{matrix}} & \left\lbrack {{Equation}6} \right\rbrack\end{matrix}$

As a result of the calculation of Equation 6, transform coefficients c₁to c_(R) for the target block may be derived. That is, when R=16,transform coefficients c₁ to c₁₆ for the target block may be derived.If, instead of RST, a regular transform is applied and a transformmatrix of 64×64 (N×N) size is multiplied to residual samples of 64×1(N×1) size, then only 16 (R) transform coefficients are derived for thetarget block because RST was applied, although 64 (N) transformcoefficients are derived for the target block. Since the total number oftransform coefficients for the target block is reduced from N to R, theamount of data transmitted by the encoding apparatus 200 to the decodingapparatus 300 decreases, so efficiency of transmission between theencoding apparatus 200 and the decoding apparatus 300 can be improved.

When considered from the viewpoint of the size of the transform matrix,the size of the regular transform matrix is 64×64 (N×N), but the size ofthe reduced transform matrix is reduced to 16×64 (R×N), so memory usagein a case of performing the RST can be reduced by an R/N ratio whencompared with a case of performing the regular transform. In addition,when compared to the number of multiplication calculations N×N in a caseof using the regular transform matrix, the use of the reduced transformmatrix can reduce the number of multiplication calculations by the R/Nratio (R×N).

In an example, the transformer 232 of the encoding apparatus 200 mayderive transform coefficients for the target block by performing theprimary transform and the RST-based secondary transform on residualsamples for the target block. These transform coefficients may betransferred to the inverse transformer of the decoding apparatus 300,and the inverse transformer 322 of the decoding apparatus 300 may derivethe modified transform coefficients based on the inverse reducedsecondary transform (RST) for the transform coefficients, and may deriveresidual samples for the target block based on the inverse primarytransform for the modified transform coefficients.

The size of the inverse RST matrix TN×R according to an example is N×Rless than the size N×N of the regular inverse transform matrix, and isin a transpose relationship with the reduced transform matrix T_(R×N)shown in Equation 4.

The matrix Tt in the Reduced Inv. Transform block shown in (b) of FIG. 7may mean the inverse RST matrix T_(R×N) ^(T) (the superscript T meanstranspose). When the inverse RST matrix T_(R×N) ^(T) is multiplied tothe transform coefficients for the target block as shown in (b) of FIG.7 , the modified transform coefficients for the target block or theresidual samples for the current block may be derived. The inverse RSTmatrix T_(R×N) ^(T) may be expressed as (T_(R×N))^(T) _(N×R).

More specifically, when the inverse RST is applied as the secondaryinverse transform, the modified transform coefficients for the targetblock may be derived when the inverse RST matrix T_(R×N) ^(T) ismultiplied to the transform coefficients for the target block.Meanwhile, the inverse RST may be applied as the inverse primarytransform, and in this case, the residual samples for the target blockmay be derived when the inverse RST matrix T_(R×N) ^(T) is multiplied tothe transform coefficients for the target block.

In an example, if the size of the block to which the inverse transformis applied is 8×8 and R=16 (i.e., R/N= 16/64=¼), then the RST accordingto (b) of FIG. 7 may be expressed as a matrix operation as shown inEquation 7 below.

$\begin{matrix}{\begin{bmatrix}t_{1,1} & t_{2,1} & & t_{16,1} \\t_{1,2} & t_{2,2} & \ldots & t_{16,2} \\t_{1,3} & t_{2,3} & & t_{16,3} \\ \vdots & \vdots & & \vdots \\{\vdots} & & \ddots & \vdots \\t_{1,64} & t_{2,64} & \ldots & t_{16,64}\end{bmatrix} \times \begin{bmatrix}c_{1} \\c_{2} \\ \vdots \\c_{16}\end{bmatrix}} & \left\lbrack {{Equation}7} \right\rbrack\end{matrix}$

In Equation 7, c₁ to c₁₆ may represent the transform coefficients forthe target block. As a result of the calculation of Equation 7, r_(i)representing the modified transform coefficients for the target block orthe residual samples for the target block may be derived, and theprocess of deriving r_(i) may be as in Equation 8.

$\begin{matrix}{\begin{matrix}\begin{matrix}{{for}i{from}1{to}N{}} \\{r_{i} = {0}} \\{{for}j{from}1{to}R} \\{r_{i}+={{tij}*c_{j}}}\end{matrix}\end{matrix}} & \left\lbrack {{Equation}8} \right\rbrack\end{matrix}$

As a result of the calculation of Equation 8, r₁ to r_(N) representingthe modified transform coefficients for the target block or the residualsamples for the target block may be derived. When considered from theviewpoint of the size of the inverse transform matrix, the size of theregular inverse transform matrix is 64×64 (N×N), but the size of thereduced inverse transform matrix is reduced to 64×16 (R×N), so memoryusage in a case of performing the inverse RST can be reduced by an R/Nratio when compared with a case of performing the regular inversetransform. In addition, when compared to the number of multiplicationcalculations N×N in a case of using the regular inverse transformmatrix, the use of the reduced inverse transform matrix can reduce thenumber of multiplication calculations by the R/N ratio (N×R).

A transform set configuration shown in Table 2 may also be applied to an8×8 RST. That is, the 8×8 RST may be applied according to a transformset in Table 2. Since one transform set includes two or three transforms(kernels) according to an intra prediction mode, it may be configured toselect one of up to four transforms including that in a case where nosecondary transform is applied. In a transform where no secondarytransform is applied, it may be considered to apply an identity matrix.Assuming that indexes 0, 1, 2, and 3 are respectively assigned to thefour transforms (e.g., index 0 may be allocated to a case where anidentity matrix is applied, that is, a case where no secondary transformis applied), a transform index or an lfnst index as a syntax element maybe signaled for each transform coefficient block, thereby designating atransform to be applied. That is, for a top-left 8×8 block, through thetransform index, it is possible to designate an 8×8 RST in an RSTconfiguration, or to designate an 8×8 lfnst when the LFNST is applied.The 8×8 lfnst and the 8×8 RST refer to transforms applicable to an 8×8region included in the transform coefficient block when both W and H ofthe target block to be transformed are equal to or greater than 8, andthe 8×8 region may be a top-left 8×8 region in the transform coefficientblock. Similarly, a 4×4 lfnst and a 4×4 RST refer to transformsapplicable to a 4×4 region included in the transform coefficient blockwhen both W and H of the target block to are equal to or greater than 4,and the 4×4 region may be a top-left 4×4 region in the transformcoefficient block.

According to an embodiment of the present disclosure, for a transform inan encoding process, only 48 pieces of data may be selected and amaximum 16×48 transform kernel matrix may be applied thereto, ratherthan applying a 16×64 transform kernel matrix to 64 pieces of dataforming an 8×8 region. Here, “maximum” means that m has a maximum valueof 16 in an m×48 transform kernel matrix for generating m coefficients.That is, when an RST is performed by applying an m×48 transform kernelmatrix (m≤16) to an 8×8 region, 48 pieces of data are input and mcoefficients are generated. When m is 16, 48 pieces of data are inputand 16 coefficients are generated. That is, assuming that 48 pieces ofdata form a 48×1 vector, a 16×48 matrix and a 48×1 vector aresequentially multiplied, thereby generating a 16×1 vector. Here, the 48pieces of data forming the 8×8 region may be properly arranged, therebyforming the 48×1 vector. For example, a 48×1 vector may be constructedbased on 48 pieces of data constituting a region excluding the bottomright 4×4 region among the 8×8 regions. Here, when a matrix operation isperformed by applying a maximum 16×48 transform kernel matrix, 16modified transform coefficients are generated, and the 16 modifiedtransform coefficients may be arranged in a top-left 4×4 regionaccording to a scanning order, and a top-right 4×4 region and abottom-left 4×4 region may be filled with zeros.

For an inverse transform in a decoding process, the transposed matrix ofthe foregoing transform kernel matrix may be used. That is, when aninverse RST or LFNST is performed in the inverse transform processperformed by the decoding apparatus, input coefficient data to which theinverse RST is applied is configured in a one-dimensional vectoraccording to a predetermined arrangement order, and a modifiedcoefficient vector obtained by multiplying the one-dimensional vectorand a corresponding inverse RST matrix on the left of theone-dimensional vector may be arranged in a two-dimensional blockaccording to a predetermined arrangement order.

In summary, in the transform process, when an RST or LFNST is applied toan 8×8 region, a matrix operation of 48 transform coefficients intop-left, top-right, and bottom-left regions of the 8×8 region excludingthe bottom-right region among transform coefficients in the 8×8 regionand a 16×48 transform kernel matrix. For the matrix operation, the 48transform coefficients are input in a one-dimensional array. When thematrix operation is performed, 16 modified transform coefficients arederived, and the modified transform coefficients may be arranged in thetop-left region of the 8×8 region.

On the contrary, in the inverse transform process, when an inverse RSTor LFNST is applied to an 8×8 region, 16 transform coefficientscorresponding to a top-left region of the 8×8 region among transformcoefficients in the 8×8 region may be input in a one-dimensional arrayaccording to a scanning order and may be subjected to a matrix operationwith a 48×16 transform kernel matrix. That is, the matrix operation maybe expressed as (48×16 matrix)*(16×1 transform coefficient vector)=(48×1modified transform coefficient vector). Here, an n×1 vector may beinterpreted to have the same meaning as an n×1 matrix and may thus beexpressed as an n×1 column vector. Further, * denotes matrixmultiplication. When the matrix operation is performed, 48 modifiedtransform coefficients may be derived, and the 48 modified transformcoefficients may be arranged in top-left, top-right, and bottom-leftregions of the 8×8 region excluding a bottom-right region.

When a secondary inverse transform is based on an RST, the inversetransformer 235 of the encoding apparatus 200 and the inversetransformer 322 of the decoding apparatus 300 may include an inversereduced secondary transformer to derive modified transform coefficientsbased on an inverse RST on transform coefficients and an inverse primarytransformer to derive residual samples for the target block based on aninverse primary transform for the modified transform coefficients. Theinverse primary transform refers to the inverse transform of a primarytransform applied to a residual. In the present disclosure, deriving atransform coefficient based on a transform may refer to deriving thetransform coefficient by applying the transform.

The above-described non-separated transform, the LFNST, will bedescribed in detail as follows. The LFNST may include a forwardtransform by the encoding apparatus and an inverse transform by thedecoding apparatus.

The encoding apparatus receives a result (or a part of a result) derivedafter applying a primary (core) transform as an input, and applies aforward secondary transform (secondary transform).

y=G ^(T) x  [Equation 9]

In Equation 9, x and y are inputs and outputs of the secondarytransform, respectively, and G is a matrix representing the secondarytransform, and transform basis vectors are composed of column vectors.In the case of an inverse LFNST, when the dimension of thetransformation matrix G is expressed as [number of rows×number ofcolumns], in the case of an forward LFNST, the transposition of matrix Gbecomes the dimension of G^(T).

For the inverse LFNST, the dimensions of matrix G are [48×16], [48×8],[16×16], [16×8], and the [48×8] matrix and the [16×8] matrix are partialmatrices that sampled 8 transform basis vectors from the left of the[48×16] matrix and the [16×16] matrix, respectively.

On the other hand, for the forward LFNST, the dimensions of matrix G^(T)are [16×48], [8×48], [16×16], [8×16], and the [8×48] matrix and the[8×16] matrix are partial matrices obtained by sampling 8 transformbasis vectors from the top of the [16×48] matrix and the [16×16] matrix,respectively.

Therefore, in the case of the forward LFNST, a [48×1] vector or [16×1]vector is possible as an input x, and a [16×1] vector or a [8×1] vectoris possible as an output y. In video coding and decoding, the output ofthe forward primary transform is two-dimensional (2D) data, so toconstruct the [48×1] vector or the [16×1] vector as the input x, aone-dimensional vector must be constructed by properly arranging the 2Ddata that is the output of the forward transformation.

FIG. 8 is a diagram illustrating a sequence of arranging output data ofa forward primary transformation into a one-dimensional vector accordingto an example. The left diagrams of (a) and (b) of FIG. 8 show thesequence for constructing a [48×1] vector, and the right diagrams of (a)and (b) of FIG. 8 shows the sequence for constructing a [16×1] vector.In the case of the LFNST, a one-dimensional vector x can be obtained bysequentially arranging 2D data in the same order as in (a) and (b) ofFIG. 8 .

The arrangement direction of the output data of the forward primarytransform may be determined according to an intra prediction mode of thecurrent block. For example, when the intra prediction mode of thecurrent block is in the horizontal direction with respect to thediagonal direction, the output data of the forward primary transform maybe arranged in the order of (a) of FIG. 8 , and when the intraprediction mode of the current block is in the vertical direction withrespect to the diagonal direction, the output data of the forwardprimary transform may be arranged in the order of (b) of FIG. 8 .

According to an example, an arrangement order different from thearrangement orders of (a) and (b) FIG. 8 may be applied, and in order toderive the same result (y vector) as when the arrangement orders of (a)and (b) FIG. 8 is applied, the column vectors of the matrix G may berearranged according to the arrangement order. That is, it is possibleto rearrange the column vectors of G so that each element constitutingthe x vector is always multiplied by the same transform basis vector.

Since the output y derived through Equation 9 is a one-dimensionalvector, when two-dimensional data is required as input data in theprocess of using the result of the forward secondary transformation asan input, for example, in the process of performing quantization orresidual coding, the output y vector of Equation 9 must be properlyarranged as 2D data again.

FIG. 9 is a diagram illustrating a sequence of arranging output data ofa forward secondary transform into a two-dimensional block according toan example.

In the case of the LFNST, output values may be arranged in a 2D blockaccording to a predetermined scan order. (a) of FIG. 8 shows that whenthe output y is a [16×1] vector, the output values are arranged at 16positions of the 2D block according to a diagonal scan order. (b) ofFIG. 8 shows that when the output y is a [8×1] vector, the output valuesare arranged at 8 positions of the 2D block according to the diagonalscan order, and the remaining 8 positions are filled with zeros. X in(b) of FIG. 8 indicates that it is filled with zero.

According to another example, since the order in which the output vectory is processed in performing quantization or residual coding may bepreset, the output vector y may not be arranged in the 2D block as shownin FIG. 9 . However, in the case of the residual coding, data coding maybe performed in 2D block (eg, 4×4) units such as CG (Coefficient Group),and in this case, the data are arranged according to a specific order asin the diagonal scan order of FIG. 9 .

Meanwhile, the decoding apparatus may configure the one-dimensionalinput vector y by arranging two-dimensional data output through adequantization process or the like according to a preset scan order forthe inverse transformation. The input vector y may be output as theoutput vector x by the following equation.

x=Gy  [Equation 10]

In the case of the inverse LFNST, an output vector x can be derived bymultiplying an input vector y, which is a [16×1] vector or a [8×1]vector, by a G matrix. For the inverse LFNST, the output vector x can beeither a [48×1] vector or a [16×1] vector.

The output vector x is arranged in a two-dimensional block according tothe order shown in FIG. 8 and is arranged as two-dimensional data, andthis two-dimensional data becomes input data (or a part of input data)of the inverse primary transformation.

Accordingly, the inverse secondary transformation is the opposite of theforward secondary transformation process as a whole, and in the case ofthe inverse transformation, unlike in the forward direction, the inversesecondary transformation is first applied, and then the inverse primarytransformation is applied.

In the inverse LFNST, one of 8 [48×16] matrices and 8 [16×16] matricesmay be selected as the transformation matrix G. Whether to apply the[48×16] matrix or the [16×16] matrix depends on the size and shape ofthe block.

In addition, 8 matrices may be derived from four transform sets as shownin Table 2 above, and each transform set may consist of two matrices.Which transform set to use among the 4 transform sets is determinedaccording to the intra prediction mode, and more specifically, thetransform set is determined based on the value of the intra predictionmode extended by considering the Wide Angle Intra Prediction (WAIP).Which matrix to select from among the two matrices constituting theselected transform set is derived through index signaling. Morespecifically, 0, 1, and 2 are possible as the transmitted index value, 0may indicate that the LFNST is not applied, and 1 and 2 may indicate anyone of two transform matrices constituting a transform set selectedbased on the intra prediction mode value.

FIG. 10 is a diagram illustrating wide-angle intra prediction modesaccording to an embodiment of the present document.

The general intra prediction mode value may have values from 0 to 66 and81 to 83, and the intra prediction mode value extended due to WAIP mayhave a value from −14 to 83 as shown. Values from 81 to 83 indicate theCCLM (Cross Component Linear Model) mode, and values from −14 to −1 andvalues from 67 to 80 indicate the intra prediction mode extended due tothe WAIP application.

When the width of the prediction current block is greater than theheight, the upper reference pixels are generally closer to positionsinside the block to be predicted. Therefore, it may be more accurate topredict in the bottom-left direction than in the top-right direction.Conversely, when the height of the block is greater than the width, theleft reference pixels are generally close to positions inside the blockto be predicted. Therefore, it may be more accurate to predict in thetop-right direction than in the bottom-left direction. Therefore, it maybe advantageous to apply remapping, ie, mode index modification, to theindex of the wide-angle intra prediction mode.

When the wide-angle intra prediction is applied, information on theexisting intra prediction may be signaled, and after the information isparsed, the information may be remapped to the index of the wide-angleintra prediction mode. Therefore, the total number of the intraprediction modes for a specific block (eg, a non-square block of aspecific size) may not change, and that is, the total number of theintra prediction modes is 67, and intra prediction mode coding for thespecific block may not be changed.

Table 3 below shows a process of deriving a modified intra mode byremapping the intra prediction mode to the wide-angle intra predictionmode.

TABLE 3 Inputs to this process are: - a variable predModeIntraspecifying the intra prediction mode, - a variable nTbW specifying thetransform block width, - a variable nTbH specifying the transform blockheight, - a variable cIdx specifying the colour component of the currentblock. Output of this process is the modified intra prediction modepredModeIntra. The variables nW and nH are derived as follows: - IfIntraSubPartitionsSplitType is equal to ISP_NO_SPLIT or cIdx is notequal to 0, the following applies:   nW = nTbW  (8-97)   nH = nTbH (8-98) - Otherwise ( IntraSubPartitionsSplitType is not equal toISP_NO_SPLIT and cIdx is equal to 0 ), the   following applies:   nW =nCbW  (8-99)   nH = nCbH (8-100) The variable whRatio is set equal toAbs( Log2( nW / nH ) ). For non-square blocks (nW is not equal to nH),the intra prediction mode predModeIntra is modified as follows: - If allof the following conditions are true, predModeIntra is set equal to (predModeIntra + 65 ).  - nW is greater than nH  - predModeIntra isgreater than or equal to 2  - predModeIntra is less than ( whRatio > 1 )? ( 8 + 2 * whRatio ) : 8 - Otherwise, if all of the followingconditions are true, predModeIntra is set equal to   ( predModeIntra −67 ).  - nH is greater than nW  - predModeIntra is less than or equal to66  - predModeIntra is greater than ( whRatio > 1 ) ? ( 60 − 2 * whRatio) : 60

In Table 3, the extended intra prediction mode value is finally storedin the predModeIntra variable, and ISP_NO_SPLIT indicates that the CUblock is not divided into sub-partitions by the Intra Sub Partitions(ISP) technique currently adopted in the VVC standard, and the cIdxvariable Values of 0, 1, and 2 indicate the case of luma, Cb, and Crcomponents, respectively. Log 2 function shown in Table 3 returns a logvalue with a base of 2, and the Abs function returns an absolute value.

Variable predModeIntra indicating the intra prediction mode and theheight and width of the transform block, etc. are used as input valuesof the wide angle intra prediction mode mapping process, and the outputvalue is the modified intra prediction mode predModeIntra. The heightand width of the transform block or the coding block may be the heightand width of the current block for remapping of the intra predictionmode. At this time, the variable whRatio reflecting the ratio of thewidth to the width may be set to Abs(Log 2(nW/nH)).

For a non-square block, the intra prediction mode may be divided intotwo cases and modified.

First, if all conditions (1)˜(3) are satisfied, (1) the width of thecurrent block is greater than the height, (2) the intra prediction modebefore modifying is equal to or greater than 2, (3) the intra predictionmode is less than the value derived from (8+2*whRatio) when the variablewhRatio is greater than 1, and is less than 8 when the variable whRatiois less than or equal to 1 [predModeIntra is less than(whRatio>1)?(8+2*whRatio): 8], the intra prediction mode is set to avalue 65 greater than the intra prediction mode [predModeIntra is setequal to (predModeIntra+65)].

If different from the above, that is, follow conditions (1)˜(3) aresatisfied, (1) the height of the current block is greater than thewidth, (2) the intra prediction mode before modifying is less than orequal to 66, (3) the intra prediction mode is greater than the valuederived from (60−2*whRatio) when the variable whRatio is greater than 1,and is greater than 60 when the variable whRatio is less than or equalto 1 [predModeIntra is greater than (whRatio>1)?(60-2*whRatio): 60], theintra prediction mode is set to a value 67 smaller than the intraprediction mode [predModeIntra is set equal to (predModeIntra-67)].

Table 2 above shows how a transform set is selected based on the intraprediction mode value extended by the WAIP in the LFNST. As shown inFIG. 10 , modes 14 to 33 and modes 35 to 80 are symmetric with respectto the prediction direction around mode 34. For example, mode 14 andmode 54 are symmetric with respect to the direction corresponding tomode 34. Therefore, the same transform set is applied to modes locatedin mutually symmetrical directions, and this symmetry is also reflectedin Table 2.

Meanwhile, it is assumed that forward LFNST input data for mode 54 issymmetrical with the forward LFNST input data for mode 14. For example,for mode 14 and mode 54, the two-dimensional data is rearranged intoone-dimensional data according to the arrangement order shown in (a) ofFIG. 8 and (b) of FIG. 8 , respectively. In addition, it can be seenthat the patterns in the order shown in (a) of FIG. 8 and (b) of FIG. 8are symmetrical with respect to the direction (diagonal direction)indicated by Mode 34.

Meanwhile, as described above, which transform matrix of the [48×16]matrix and the [16×16] matrix is applied to the LFNST is determined bythe size and shape of the transform target block.

FIG. 11 is a diagram illustrating a block shape to which the LFNST isapplied. (a) of FIG. 11 shows 4×4 blocks, (b) shows 4×8 and 8×4 blocks,(c) shows 4×N or N×4 blocks in which N is 16 or more, (d) shows 8×8blocks, (e) shows M×N blocks where M≥8, N≥8, and N>8 or M>8.

In FIG. 11 , blocks with thick borders indicate regions to which theLFNST is applied. For the blocks of (a) and (b) of FIG. 11 , the LFNSTis applied to the top-left 4×4 region, and for the block of (c) of FIG.11 , the LFNST is applied individually the two top-left 4×4 regions arecontinuously arranged. In (a), (b), and (c) of FIG. 11 , since the LFNSTis applied in units of 4×4 regions, this LFNST will be hereinafterreferred to as “4×4 LFNST”. Based on the matrix dimension for G, a[16×16] or [16×8] matrix may be applied.

More specifically, the [16×8] matrix is applied to the 4×4 block (4×4 TUor 4×4 CU) of (a) of FIG. 11 and the [16×16] matrix is applied to theblocks in (b) and (c) of FIG. 11 . This is to adjust the computationalcomplexity for the worst case to 8 multiplications per sample.

With respect to (d) and (e) of FIG. 11 , the LFNST is applied to thetop-left 8×8 region, and this LFNST is hereinafter referred to as “8×8LFNST”. As a corresponding transformation matrix, a [48×16] matrix or[48×8] matrix may be applied. In the case of the forward LFNST, sincethe [48×1] vector (x vector in Equation 9) is input as input data, allsample values of the top-left 8×8 region are not used as input values ofthe forward LFNST. That is, as can be seen in the left order of (a) ofFIG. 8 or the left order of (b) of FIG. 8 , the [48×1] vector may beconstructed based on samples belonging to the remaining 3 4×4 blockswhile leaving the bottom-right 4×4 block as it is.

The [48×8] matrix may be applied to an 8×8 block (8×8 TU or 8×8 CU) in(d) of FIG. 11 , and the [48×16] matrix may be applied to the 8×8 blockin (e) of FIG. 11 . This is also to adjust the computational complexityfor the worst case to 8 multiplications per sample.

Depending on the block shape, when the corresponding forward LFNST (4×4LFNST or 8×8 LFNST) is applied, 8 or 16 output data (y vector inEquation 9, [8×1] or [16×1] vector) is generated. In the forward LFNST,the number of output data is equal to or less than the number of inputdata due to the characteristics of the matrix G^(T).

FIG. 12 is a diagram illustrating an arrangement of output data of aforward LFNST according to an example, and shows a block in which outputdata of the forward LFNST is arranged according to a block shape.

The shaded area at the top-left of the block shown in FIG. 12corresponds to the area where the output data of the forward LFNST islocated, the positions marked with 0 indicate samples filled with avalue of 0, and the remaining area represents regions that are notchanged by the forward LFNST. In the area not changed by the LFNST, theoutput data of the forward primary transform remains unchanged.

As described above, since the dimension of the transform matrix appliedvaries according to the shape of the block, the number of output dataalso varies. As FIG. 12 , the output data of the forward LFNST may notcompletely fill the top-left 4×4 block. In the case of (a) and (d) ofFIG. 12 , a [16×8] matrix and a [48×8] matrix are applied to the blockindicated by a thick line or a partial region inside the block,respectively, and a [8×1] vector as the output of the forward LFNST isgenerated. That is, according to the scan order shown in (b) of FIG. 9 ,only 8 output data may be filled as shown in (a) and (d) of FIG. 12 ,and 0 may be filled in the remaining 8 positions. In the case of theLFNST applied block of (d) of FIG. 11 , as shown in (d) of FIG. 12 , two4×4 blocks in the top-right and bottom-left adjacent to the top-left 4×4block are also filled with a value of 0.

As described above, basically, by signaling the LFNST index, whether toapply the LFNST and the transform matrix to be applied are specified. Asshown FIG. 12 , when the LFNST is applied, since the number of outputdata of the forward LFNST may be equal to or less than the number ofinput data, a region filled with a zero value occurs as follows.

1) As shown in (a) of FIG. 12 , samples from the 8th and later positionsin the scan order in the top-left 4×4 block, that is, samples from the9th to the 16th.

2) As shown in (d) and (e) of FIG. 12 , when the [48×16] matrix or the[48×8] matrix is applied, two 4×4 blocks adjacent to the top-left 4×4block or the second and third 4×4 blocks in the scan order.

Therefore, if non-zero data exists by checking the areas 1) and 2), itis certain that the LFNST is not applied, so that the signaling of thecorresponding LFNST index can be omitted.

According to an example, for example, in the case of LFNST adopted inthe VVC standard, since signaling of the LFNST index is performed afterthe residual coding, the encoding apparatus may know whether there isthe non-zero data (significant coefficients) for all positions withinthe TU or CU block through the residual coding. Accordingly, theencoding apparatus may determine whether to perform signaling on theLFNST index based on the existence of the non-zero data, and thedecoding apparatus may determine whether the LFNST index is parsed. Whenthe non-zero data does not exist in the area designated in 1) and 2)above, signaling of the LFNST index is performed.

Meanwhile, for the adopted LFNST, the following simplification methodsmay be applied.

(i) According to an example, the number of output data for the forwardLFNST may be limited to a maximum of 16.

In the case of (c) of FIG. 11 , the 4×4 LFNST may be applied to two 4×4regions adjacent to the top-left, respectively, and in this case, amaximum of 32 LFNST output data may be generated. when the number ofoutput data for forward LFNST is limited to a maximum of 16, in the caseof 4×N/N×4 (N≥16) blocks (TU or CU), the 4×4 LFNST is only applied toone 4×4 region in the top-left, the LFNST may be applied only once toall blocks of FIG. 11 . Through this, the implementation of image codingmay be simplified.

(ii) According to an example, zero-out may be additionally applied to aregion to which the LFNST is not applied. In this document, the zero-outmay mean filling values of all positions belonging to a specific regionwith a value of 0. That is, the zero-out can be applied to a region thatis not changed due to the LFNST and maintains the result of the forwardprimary transformation. As described above, since the LFNST is dividedinto the 4×4 LFNST and the 8×8 LFNST, the zero-out can be divided intotwo types ((ii)-(A) and (ii)-(B)) as follows.

(ii)-(A) When the 4×4 LFNST is applied, a region to which the 4×4 LFNSTis not applied may be zeroed out. FIG. 13 is a diagram illustrating thezero-out in a block to which the 4×4 LFNST is applied according to anexample.

As shown in FIG. 13 , with respect to a block to which the 4×4 LFNST isapplied, that is, for all of the blocks in (a), (b) and (c) of FIG. 11 ,the whole region to which the LFNST is not applied may be filled withzeros.

On the other hand, (d) of FIG. 13 shows that when the maximum value ofthe number of the output data of the forward LFNST is limited to 16according to an example, the zero-out is performed on the remainingblocks to which the 4×4 LFNST is not applied.

(ii)-(B) When the 8×8 LFNST is applied, a region to which the 8×8 LFNSTis not applied may be zeroed out. FIG. 14 is a diagram illustrating thezero-out in a block to which the 8×8 LFNST is applied according to anexample.

As shown in FIG. 14 , with respect to a block to which the 8×8 LFNST isapplied, that is, for all of the blocks in (d) and (e) of FIG. 12 , thewhole region to which the LFNST is not applied may be filled with zeros.

(iii) Due to the zero-out presented in (ii) above, the area filled withzeros may be not same when the LFNST is applied. Accordingly, it ispossible to check whether the non-zero data exists according to thezero-out proposed in (ii) over a wider area than the case of the LFNSTof FIG. 12 .

For example, when (ii)-(B) is applied, after checking whether thenon-zero data exists where the area filled with zero values in (d) and(e) of FIG. 12 in addition to the area filled with 0 additionally inFIG. 14 , signaling for the LFNST index can be performed only when thenon-zero data does not exist.

Of course, even if the zero-out proposed in (ii) is applied, it ispossible to check whether the non-zero data exists in the same way asthe existing LFNST index signaling. That is, after checking whether thenon-zero data exists in the block filled with zeros in FIG. 12 , theLFNST index signaling may be applied. In this case, the encodingapparatus only performs the zero out and the decoding apparatus does notassume the zero out, that is, checking only whether the non-zero dataexists only in the area explicitly marked as 0 in FIG. 12 , may performthe LFNST index parsing.

Various embodiments in which combinations of the simplification methods((i), (ii)-(A), (ii)-(B), (iii)) for the LFNST are applied may bederived. Of course, the combinations of the above simplification methodsare not limited to the following an embodiment, and any combination maybe applied to the LFNST.

EMBODIMENT

-   -   Limit the number of output data for forward LFNST to a maximum        of 16 (i)    -   When the 4×4 LFNST is applied, all areas to which the 4×4 LFNST        is not applied are zero-out→(ii)-(A)    -   When the 8×8 LFNST is applied, all areas to which the 8×8 LFNST        is not applied are zero-out→(ii)-(B)    -   After checking whether the non-zero data exists also the        existing area filled with zero value and the area filled with        zeros due to additional zero outs ((ii)-(A), (ii)-(B)), the        LFNST index is signaled only when the non-zero data does not        exist→(iii)

In the case of the Embodiment, when the LFNST is applied, an area inwhich the non-zero output data can exist is limited to the inside of thetop-left 4×4 area. In more detail, in the case of (a) of FIG. 13 and (a)of FIG. 14 , the 8th position in the scan order is the last positionwhere non-zero data can exist. In the case of (b) and (c) of FIG. 13 and(b) of FIG. 14 , the 16th position in the scan order (ie, the positionof the bottom-right edge of the top-left 4×4 block) is the last positionwhere data other than 0 may exist.

Therefore, when the LFNST is applied, after checking whether thenon-zero data exists in a position where the residual coding process isnot allowed (at a position beyond the last position), it can bedetermined whether the LFNST index is signaled.

In the case of the zero-out method proposed in (ii), since the number ofdata finally generated when both the primary transform and the LFNST areapplied, the amount of computation required to perform the entiretransformation process can be reduced. That is, when the LFNST isapplied, since zero-out is applied to the forward primary transformoutput data existing in a region to which the LFNST is not applied,there is no need to generate data for the region that become zero-outduring performing the forward primary transform. Accordingly, it ispossible to reduce the amount of computation required to generate thecorresponding data. The additional effects of the zero-out methodproposed in (ii) are summarized as follows.

First, as described above, the amount of computation required to performthe entire transform process is reduced.

In particular, when (ii)-(B) is applied, the amount of calculation forthe worst case is reduced, so that the transform process can belightened. In other words, in general, a large amount of computation isrequired to perform a large-size primary transformation. By applying(ii)-(B), the number of data derived as a result of performing theforward LFNST can be reduced to 16 or less. In addition, as the size ofthe entire block (TU or CU) increases, the effect of reducing the amountof transform operation is further increased.

Second, the amount of computation required for the entire transformprocess can be reduced, thereby reducing the power consumption requiredto perform the transform.

Third, the latency involved in the transform process is reduced.

The secondary transformation such as the LFNST adds a computationalamount to the existing primary transformation, thus increasing theoverall delay time involved in performing the transformation. Inparticular, in the case of intra prediction, since reconstructed data ofneighboring blocks is used in the prediction process, during encoding,an increase in latency due to a secondary transformation leads to anincrease in latency until reconstruction. This can lead to an increasein overall latency of intra prediction encoding.

However, if the zero-out suggested in (ii) is applied, the delay time ofperforming the primary transform can be greatly reduced when LFNST isapplied, the delay time for the entire transform is maintained orreduced, so that the encoding apparatus can be implemented more simply.

In the conventional intra prediction, a block to be currently encoded isregarded as one encoding unit and encoding was performed withoutsplitting. However, intra sub-partitions (ISP) coding means performingintra prediction encoding by dividing a block to be currently encoded ina horizontal direction or a vertical direction. In this case, areconstructed block may be generated by performing encoding/decoding inunits of divided blocks, and the reconstructed block may be used as areference block of the next divided block. According to an embodiment,in ISP coding, one coding block may be divided into two or foursub-blocks and coded, and in ISP, in one sub-block, intra prediction isperformed with reference to a reconstructed pixel value of a sub-blocklocated at the adjacent left side or adjacent upper side. Hereinafter,“coding” may be used as a concept including both coding performed by anencoding apparatus and decoding performed by a decoding apparatus.

The ISP is to divide a block predicted as luma intra into two or foursub-partitions in a vertical direction or a horizontal directionaccording to the size of the block. For example, the minimum block sizeto which the ISP can be applied is 4×8 or 8×4. When the block size isgreater than 4×8 or 8×4, the block is divided into 4 sub-partitions.

When ISP is applied, sub-blocks are sequentially coded, for example,horizontally or vertically, from left to right or from top to bottomaccording to a division type, and after a reconstruction process isperformed via inverse transform and intra prediction for one sub-block,coding for the next sub-block may be performed. For the leftmost oruppermost subblock, a reconstructed pixel of the already coded codingblock is referred to, as in a conventional intra prediction method.Further, when each side of a subsequent internal sub-block is notadjacent to a previous sub-block, in order to derive reference pixelsadjacent to the corresponding side, reconstructed pixels of an alreadycoded adjacent coding block are referred to, as in a conventional intraprediction method.

In the ISP coding mode, all sub-blocks may be coded with the same intraprediction mode, and a flag indicating whether to use ISP coding and aflag indicating whether to divide (horizontally or vertically) in whichdirection may be signaled. At this time, the number of sub-blocks may beadjusted to 2 or 4 according to a block shape, and when the size(width×height) of one sub-block is less than 16, it may be restricted sothat division into the corresponding sub-block is not allowed or the ISPcoding itself is not applied.

In the case of the ISP prediction mode, one coding unit is divided intotwo or four partition blocks, that is, sub-blocks and predicted, and thesame intra prediction mode is applied to the divided two or fourpartition blocks.

As described above, in the division direction, the horizontal direction(when an M×N coding unit having horizontal and vertical lengths of M andN, respectively, is divided in the horizontal direction, if the M×Ncoding unit is divided into two, the M×N coding unit is divided intoM×(N/2) blocks, and if the M×N coding unit is divided into four blocks,the M×N coding unit is divided into M×(N/4) blocks) and the verticaldirection (when an M×N coding unit is divided in a vertical direction,if the M×N coding unit is divided into two, and the M×N coding unit isdivided into (M/2)×N blocks, and if the M×N coding unit is divided intofour, the M×N coding unit is divided into (M/4)×N blocks) are bothpossible. When the M×N coding unit is divided in the horizontaldirection, partition blocks are coded in a top-down order, and when theM×N coding unit is divided in the vertical direction, partition blocksare coded in order from left to right. The currently coded partitionblock may be predicted with reference to the reconstructed pixel valuesof the upper (left) partition block in the case of horizontal (vertical)direction division.

A transform may be applied to a residual signal generated by the ISPprediction method in units of partition blocks. Multiple transformselection (MTS) technology based on a DST-7/DCT-8 combination as well asthe existing DCT-2 may be applied to a primary transform (coretransform) based on a forward direction, and a forward low frequencynon-separable transform (LFNST) may be applied to transform coefficientsgenerated according to the primary transform to generate a finalmodified transform coefficient.

That is, an LFNST may be applied to partition blocks divided by applyingan ISP prediction mode, and the same intra prediction mode is applied tothe divided partition blocks, as described above. Accordingly, when theLFNST set derived based on the intra prediction mode is selected, thederived LFNST set may be applied to all partition blocks. That is,because the same intra prediction mode is applied to all partitionblocks, the same LFNST set may be applied to all partition blocks.

According to an embodiment, an LFNST may be applied only to transformblocks having both a horizontal length and a vertical length of 4 ormore. Therefore, when the horizontal or vertical length of the dividedpartition block according to the ISP prediction method is less than 4,the LFNST is not applied and an LFNST index is not signaled. Further,when the LFNST is applied to each partition block, the correspondingpartition block may be regarded as one transform block. When the ISPprediction method is not applied, the LFNST may be applied to the codingblock.

A method of applying an LFNST to each partition block will be describedin detail.

According to an embodiment, after a forward LFNST is applied toindividual partition blocks, only maximum 16 (8 or 16) coefficients areleft in the top-left 4×4 region in transform coefficient scanning order,and then zero out in which the remaining positions and regions are allfilled with a value of 0 may be applied.

Alternatively, according to an embodiment, when a length of one side ofthe partition block is 4, the LFNST is applied only to the top-left 4×4region, and when a length of all sides of the partition block, that is,the width and height is 8 or more, the LFNST may be applied to theremaining 48 coefficients, except for a bottom-right 4×4 region inside atop-left 8×8 region.

Alternatively, according to an embodiment, in order to adjustcomputational complexity of the worst case to 8 multiplications persample, when each partition block is 4×4 or 8×8, only 8 transformcoefficients may be output after applying the forward LFNST. That is,when the partition block is 4×4, an 8×16 matrix may be applied as atransform matrix, and when the partition block is 8×8, an 8×48 matrixmay be applied as a transform matrix.

In the current VVC standard, LFNST index signaling is performed in unitsof coding units. Therefore, in the ISP prediction mode and when an LFNSTis applied to all partition blocks, the same LFNST index value may beapplied to the corresponding partition blocks. That is, when the LFNSTindex value is transmitted once at a coding unit level, thecorresponding LFNST index may be applied to all partition blocks in thecoding unit. As described above, the LFNST index value may have valuesof 0, 1, and 2, where 0 represents a case in which an LFNST is notapplied, and 1 and 2 indicate two transform matrices existing in oneLFNST set when an LFNST is applied.

As described above, the LFNST set is determined by the intra predictionmode, and in the case of the ISP prediction mode, because all partitionblocks in the coding unit are predicted in the same intra predictionmode, the partition blocks may refer to the same LFNST set.

As another example, LFNST index signaling is still performed in units ofa coding unit, but in the case of the ISP prediction mode, whether touniformly apply an LFNST to all partition blocks is not determined, andfor each partition block, whether to apply the LFNST index valuesignaled at a coding unit level or whether not to apply the LFNST may bedetermined through a separate condition. Here, a separate condition maybe signaled in the form of a flag for each partition block through abitstream, and when a flag value is 1, an LFNST index value signaled atthe coding unit level is applied, and when a flag value is 0, the LFNSTmay not be applied.

Hereinafter, a method of maintaining the computational complexity forthe worst case when LFNST is applied to the ISP mode will be described.

In the case of an ISP mode, when LFNST is applied, in order to maintainthe number of multiplications per sample (or per coefficient, perposition) to a certain value or less, the application of LFNST may belimited. According to the size of the partition block, the number ofmultiplications per sample (or per coefficient, per position) may bemaintained to 8 or less by applying LFNST as follows.

When both a horizontal length and a vertical length of the partitionblock are 4 or more, the same method as a calculation complexity controlmethod for the worst case for LFNST in the current VVC standard may beapplied.

That is, when the partition block is a 4×4 block, instead of a 16×16matrix, an 8×16 matrix obtained by sampling the top 8 rows from a 16×16matrix may be applied in a forward direction, and a 16×8 matrix obtainedby sampling the left 8 columns from a 16×16 matrix may be applied in areverse direction. Further, when the partition block is 8×8 blocks, inthe forward direction, instead of a 16×48 matrix, an 8×48 matrixobtained by sampling the top 8 rows from a 16×48 matrix is applied, andin the reverse direction, instead of a 48×16 matrix, a 48×8 matrixobtained by sampling the left 8 columns from a 48×16 matrix may beapplied.

In the case of a 4×N or N×4 (N>4) block, when a forward transform isperformed, 16 coefficients generated after applying a 16×16 matrix toonly the top-left 4×4 block may be disposed in the top-left 4×4 region,and other regions may be filled with a value of 0. Further, whenperforming an inverse transform, 16 coefficients located in the top-left4×4 block are disposed in scanning order to form an input vector, andthen 16 output data may be generated by multiplying the 16×16 matrix.The generated output data may be disposed in the top-left 4×4 region,and the remaining regions, except for the top-left 4×4 region, may befilled with a value of 0.

In the case of an 8×N or N×8 (N>8) block, when the forward transform isperformed, 16 coefficients generated after applying the 16×48 matrix toonly an ROI region (the remaining regions excluding bottom-right 4×4blocks from the top-left 8×8 blocks) inside the top-left 8×8 blocks maybe disposed in the top-left 4×4 region, and all other regions may befilled with a value of 0. Further, when performing an inverse transform,16 coefficients located in the top-left 4×4 block are disposed inscanning order to form an input vector, and then 48 output data may begenerated by multiplying the input vector by a 48×16 matrix. Thegenerated output data may be filled in the ROI region, and all otherregions may be filled with a value of 0.

As another example, in order to maintain the number of multiplicationsper sample (or per coefficient, per position) to a certain value orless, the number of multiplications per sample (or per coefficient, perposition) based on the ISP coding unit size rather than the size of theISP partition block may be maintained to 8 or less. When there is onlyone block satisfying the condition to which LFNST is applied among theISP partition blocks, the complexity calculation for the worst case ofLFNST may be applied based on the corresponding coding unit size ratherthan the size of the partition block. For example, when a luma codingblock for a certain coding unit is divided into 4 partition blocks of4×4 size and coded by ISP, and non-zero transform coefficients do notexist for two partition blocks among them, the other two partitionsblocks can be set to generate 16 transform coefficients instead of 8each (based on the encoder).

Hereinafter, a method of signaling the LFNST index in the case of theISP mode will be described.

As described above, the LFNST index may have values of 0, 1, and 2,where 0 indicates that LFNST is not applied, and 1 and 2 indicate eitherone of two LFNST kernel matrices included in the selected LFNST set. TheLFNST is applied based on the LFNST kernel matrix selected by the LFNSTindex. A method of transmitting the LFNST index in the current VVCstandard will be described as follows.

1. The LFNST index may be transmitted once for each coding unit (CU),and in the case of a dual-tree, an individual LFNST index may besignaled for a luma block and a chroma block, respectively.

2. When the LFNST index is not signaled, the LFNST index value is set(inferred) to a default value of 0. The case where the LFNST index valueis inferred to be 0 is as follows.

A. In the case of a mode (eg, transform skip, BDPCM, lossless coding,etc.) to which no transform is applied.

B. When the primary transformation is not DCT-2 (DST7 or DCT8), that is,when the transform in the horizontal direction or the transform in thevertical direction is not DCT-2

C. When the horizontal length or vertical length of the luma block ofthe coding unit exceeds the size of the maximum luma transform that canbe transformed, for example, when the size of the maximum luma transformthat can be transformed is 64, in the case where the size of the lumablock of the coding block is equal to 128×16, the LFNST cannot beapplied.

In the case of a dual tree, it is determined whether the size of themaximum luma transform is exceeded for each of the coding unit for theluma component and the coding unit for the chroma component. That is, itis checked whether the size of the maximum luma transform that can betransformed for the luma block is exceeded, and the horizontal/verticallength of the luma block corresponding to the color format for thechroma block and the size of the maximum transformable maximum lumatransform are exceeded. For example, when the color format is 4:2:0, thehorizontal/vertical length of the corresponding luma block is twice thatof the corresponding chroma block, and the transform size of thecorresponding luma block is twice that of the corresponding chromablock. As another example, when the color format is 4:4:4, thehorizontal/vertical length and transformation size of the correspondingluma block are the same as those of the corresponding chroma block.

A 64-length transformation or a 32-length transformation means atransformation applied horizontally or vertically having a length of 64or 32, respectively, and “transformation size” may mean a correspondinglength of 64 or 32.

In the case of a single tree, after checking whether a horizontal lengthor a vertical length of a luma block exceeds the maximum transformableluma transform block size, if it exceeds, the LFNST index signaling maybe omitted.

D. The LFNST index may be transmitted only when both the horizontallength and the vertical length of the coding unit are 4 or more.

In the case of the dual tree, the LFNST index can be signaled only whenboth the horizontal and vertical lengths of a corresponding component(ie, a luma or chroma component) are 4 or more.

In the case of a single tree, the LFNST index may be signaled when boththe horizontal and vertical lengths of the luma component are 4 or more.

E. When the position of the last non-zero coefficient is not a DCposition (top-left position of the block), in the case of a dual treetype luma block, if the position of the last non-zero coefficient is nota DC position, the LFNST index is transmitted. In the case of the dualtree type chroma block, if any one of the position of the last non-zerocoefficient for Cb and the position of the last non-zero coefficient forCr is not a DC position, the corresponding LNFST index is transmitted.

In the case of the single tree type, when the position of the lastnon-zero coefficient is not a DC position, the LFNST index istransmitted in any one of the luma component, the Cb component, and theCr component.

Here, when a coded block flag (CBF) value indicating whether a transformcoefficient exists for one transform block is 0, the position of thelast non-zero coefficient for the corresponding transform block is notchecked in order to determine whether the LFNST index is signaled. Thatis, when the corresponding CBF value is 0, since no transform is appliedto the corresponding block, the position of the last non-zerocoefficient may not be considered when checking the condition for LFNSTindex signaling.

For example, 1) In the case of a dual tree type and a luma component, ifthe CBF value is 0, the LFNST index is not signaled, 2) In the case of adual tree type and a chroma component, if the CBF value for Cb is 0 andthe CBF value for Cr is 1, only the position of the last non-zerocoefficient for Cr is checked and the corresponding LFNST index istransmitted, 3) In the case of a single tree type, for all of luma, Cb,and Cr, the position of the last non-zero coefficient is checked onlyfor components with each CBF value of 1.

When it is confirmed that the transform coefficient exists in a positionother than a position where the LFNST transform coefficient may exist,LFNST index signaling may be omitted. In the case of a 4×4 transformblock and an 8×8 transform block, according to the transform coefficientscanning order in the VVC standard, the LFNST transform coefficients mayexist in eight positions from the DC position, and all remainingpositions are filled with zeros. In addition, when the 4×4 transformblock and the 8×8 transform block are not, the LFNST transformcoefficients may exist in 16 positions from the DC position according tothe transform coefficient scanning order in the VVC standard, and allremaining positions are filled with zeros.

Accordingly, if non-zero transform coefficients exist in the region tobe filled with the zero value after performing residual coding, theLFNST index signaling may be omitted.

Meanwhile, the ISP mode may be applied only to the luma block or may beapplied to both the luma block and the chroma block. As described above,when the ISP prediction is applied, the corresponding coding unit isdivided into two or four partition blocks and predicted, and a transformmay be applied to the corresponding partition blocks, respectively.Therefore, when determining a condition for signaling the LFNST index inunits of coding units, it is necessary to consider the fact that LFNSTmay be applied to respective partition blocks. In addition, when the ISPprediction mode is applied only to a specific component (eg, a lumablock), the LFNST index needs to be signaled in consideration of thefact that only the corresponding component is divided into partitionblocks. The LFNST index signaling methods available in ISP mode aresummarized as follows.

1. The LFNST index may be transmitted once for each coding unit (CU),and in the case of a dual-tree, an individual LFNST index may besignaled for a luma block and a chroma block, respectively.

2. When the LFNST index is not signaled, the LFNST index value is set(inferred) to a default value of 0. The case where the LFNST index valueis inferred to be 0 is as follows.

A. In the case of a mode (eg, transform skip, BDPCM, lossless coding,etc.) to which no transform is applied

B. When the horizontal length or vertical length of the luma block ofthe coding unit exceeds the size of the maximum luma transform that canbe transformed, for example, when the size of the maximum luma transformthat can be transformed is 64, in the case where the size of the lumablock of the coding block is equal to 128×16, the LFNST cannot beapplied.

It may be determined whether the LFNST index is signaled based on thesize of the partition block instead of the coding unit. That is, whenthe horizontal length or the vertical length of the partition block forthe corresponding luma block exceeds the size of the maximum lumatransform that can be transformed, the LFNST index signaling may beomitted and the LFNST index value may be inferred to be 0.

In the case of the dual tree, it is determined whether the maximumtransform block size is exceeded for each of the coding unit orpartition block for the luma component and the coding unit or partitionblock for the chroma component. That is, if the horizontal and verticallengths of the coding unit or partition block for luma are compared withthe maximum luma transform size, respectively, and if even one is largerthan the maximum luma transform size, the LFNST is not applied, and inthe case of the coding unit or partition block for chroma, thehorizontal/vertical length of the corresponding luma block for the colorformat and the size of the maximum luma transform capable of maximumtransformation are compared. For example, when the color format is4:2:0, the horizontal/vertical length of the corresponding luma block istwice that of the corresponding chroma block, and the transform size ofthe corresponding luma block is twice that of the corresponding chromablock. As another example, when the color format is 4:4:4, thehorizontal/vertical length and transformation size of the correspondingluma block are the same as those of the corresponding chroma block.

In the case of the single tree, after checking whether a horizontallength or a vertical length of a luma block (coding unit or partitionblock) exceeds the maximum transformable luma transform block size, ifit exceeds, the LFNST index signaling may be omitted.

C. If the LFNST included in the current VVC standard is applied, theLFNST index can be transmitted only when both the horizontal andvertical lengths of the partition block are 4 or more.

If the LFNST for a 2×M (1×M) or M×2 (M×1) block is applied in additionto the LFNST included in the current VVC standard, the LFNST index canbe transmitted only when the size of the partition block is equal to orgreater than 2×M (1×M) or M×2 (M×1) blocks. Here, the meaning that theP×Q block is equal to or greater than the R×S block means that P≥r andQ≥S.

In summary, the LFNST index can be transmitted only when the partitionblock is equal to or larger than the minimum size applicable to LFNST.In the case of the dual tree, the LFNST index can be signaled only whenthe partition block for the luma or chroma component is equal to orlarger than the minimum size to which the LFNST is enable. In the caseof the single tree, the LFNST index may be signaled only when thepartition block for the luma component is equal to or larger than theminimum size applicable to LFNST.

In the present disclosure, when an M×N block is greater than or equal toa K×L block, it means that M is greater than or equal to K and N isgreater than or equal to L. The fact that the M×N block is larger thanthe K×L block means that M is greater than or equal to K and N isgreater than or equal to L, and M is greater than K or N is greater thanL. The fact that the M×N block is less than or equal to the K×L blockmeans that M is less than or equal to K and N is less than or equal toL, and the fact that the M×N block less than the K×L block means that Mis less than or equal to K and N is less than L and M is less than K orN is less than L.

When the position of the last non-zero coefficient is not the DCposition (the upper-left position of the block), if it is a luma blockof the dual tree type, in the case of the position of the last non-zerocoefficient in any of all partition blocks is not a DC position, theLFNST index may be transmitted. If it is the dual tree type and is thechroma block, when any one of the position of the last non-zerocoefficient of all partition blocks for Cb (the number of partitionblocks is considered to be one when the ISP mode is not applied to thechroma component) and the position of the last non-zero coefficient ofall partition blocks for Cr (when the ISP mode is not applied to thechroma component, the number of partition blocks is considered to beone) is not a DC position, the corresponding LNFST index may betransmitted.

In the case of the single tree type, if the position of the lastnon-zero coefficient is not the DC position of any one of all partitionblocks for the luma component, the Cb component, and the Cr component,the corresponding LFNST index may be transmitted.

Here, when a coded block flag (CBF) value indicating whether a transformcoefficient exists for each partition block is 0, the position of thelast non-zero coefficient for the corresponding partition block is notchecked in order to determine whether the LFNST index is signaled. Thatis, when the corresponding CBF value is 0, the transform is not appliedto the corresponding block, so the position of the last non-zerocoefficient for the corresponding partition block is not considered whenchecking the condition for LFNST index signaling.

For example, 1) In case of dual tree type and luma component, if thecorresponding CBF value for each partition block is 0, the correspondingpartition block is excluded when determining whether to signal the LFNSTindex, 2) in case of the dual tree type and the chroma component, foreach partition block, if the CBF value for Cb is 0 and the CBF value forCr is 1, only the position of the last non-zero coefficient for Cr ischecked to determine whether to signal the corresponding LFNST index, 3)In case of the single tree type, for all partition blocks of the lumacomponent, the Cb component, and the Cr component, whether the LFNSTindex is signaled may be determined by checking the position of the lastnon-zero coefficient only for blocks having a CBF value of 1.

In the case of the ISP mode, the image information may be configured sothat the position of the last non-zero coefficient is not checked, andan embodiment thereof is as follows.

i. In the case of the ISP mode, the LFNST index signaling may be allowedwithout checking the position of the last non-zero coefficient for boththe luma block and the chroma block. That is, even if the position ofthe last non-zero coefficient for all partition blocks is the DCposition or the corresponding CBF value is 0, the LFNST index signalingmay be allowed.

ii. In the case of the ISP mode, the check of the position of the lastnon-zero coefficient only for the luma block may be omitted, and in thecase of the chroma block, the position of the last non-zero coefficientmay be checked in the above-described manner. For example, in the caseof the dual tree type and luma block, the LFNST index signaling isallowed without checking the position of the last non-zero coefficient,and in the case of the dual tree type and chroma block, in theabove-described manner, it is possible to determine whether thecorresponding LFNST index is signaled by checking whether the DCposition exists for the position of the last non-zero coefficient.

iii. In the case of the ISP mode and the single tree type, the method ior ii above may be applied. That is, in the ISP mode and when the numberi is applied to the single tree type, it is possible to omit the checkof the position of the last non-zero coefficient for both the luma blockand the chroma block and allow LFNST index signaling. Alternatively, thenumber ii is applied to omit the check on the position of the lastnon-zero coefficient for partition blocks for the luma component, andwith respect to the partition blocks (in the case where ISP is notapplied to the chroma component, the number of partition blocks may beconsidered to be 1) for the chroma component, it is possible todetermine whether to signal the corresponding LFNST index by performinga check on the position of the last non-zero coefficient in the mannerdescribed above.

E. If it is confirmed that the transform coefficient exists in aposition other than a position where the LFNST transform coefficient mayexist even for one partition block among all partition blocks, the LFNSTindex signaling may be omitted.

For example, in the case of a 4×4 partition block and an 8×8 partitionblock, according to the transform coefficient scanning order in the VVCstandard, the LFNST transform coefficients may exist in eight positionsfrom the DC position, and all remaining positions are filled with zeros.In addition, if it is equal to or greater than 4×4 and is not a 4×4partition block and an 8×8 partition block, the LFNST transformcoefficients may exist in 16 positions from the DC position according tothe transform coefficient scanning order in the VVC standard, and allremaining positions are filled with zeros.

Accordingly, if non-zero transform coefficients exist in the region tobe filled with the zero value after performing residual coding, theLFNST index signaling may be omitted.

On the other hand, in the case of the ISP mode, the current VVC standardsees length conditions independently in the horizontal and verticaldirections, and applies DST-7 instead of DCT-2 without signaling the MTSindex. It is determined whether the horizontal or vertical length isgreater than or equal to 4 and greater than or equal to or less than 16,and a primary transform kernel is determined according to thedetermination result. Therefore, in the case of the ISP mode and in thecase where the LFNST can be applied, the following transform combinationconfiguration is possible.

1. When the LFNST index is 0 (including the case where the LFNST indexis inferred to be 0), the primary transform decision condition for theISP included in the current VVC standard may be followed. That is, itchecks whether the length condition (condition equal to or greater than4 and greater than or less than 16) is satisfied independently for eachof the horizontal and vertical directions, and if it is satisfied, forthe primary transform, the DST-7 is applied instead of the DCT-2, and ifit is not satisfied, the DCT-2 may be applied.

2. For the case where the LFNST index is greater than 0, the followingtwo configurations may be possible as the primary transform.

A. The DCT-2 may be applied to both horizontal and vertical directions.

B. The primary transform decision condition at the time of the ISPincluded in the current VVC standard may be followed. That is, it checkswhether the length condition (condition equal to or greater than 4 andgreater than or less than 16) is satisfied independently for each of thehorizontal and vertical directions, and if it is satisfied, the DST-7 isapplied instead of the DCT-2, and if it is not satisfied, the DCT-2 maybe applied.

In the ISP mode, image information may be configured such that the LFNSTindex is transmitted for each partition block rather than for eachcoding unit. In this case, in the above-described LFNST index signalingmethod, it may be considered that only one partition block exists in aunit in which the LFNST index is transmitted, and whether or not tosignal the LFNST index may be determined.

Meanwhile, the signaling of the LFNST index and the MTS index will bedescribed below.

The following table shows a coding unit syntax table, a transform unitsyntax table, and a residual coding syntax table related to thesignaling of the LFNST index and the MTS index according to an example.According to Table 4, the MTS index moves from the transform unit levelto the coding unit level syntax, and is signaled after the LFNST indexsignaling. In addition, the constraint that does not allow the LFNSTwhen the ISP is applied to the coding unit has been removed. When theISP is applied to a coding unit, the constraint that does not allow theLFNST is removed, so that the LFNST may be applied to all intraprediction blocks. In addition, both the MTS index and the LFNST indexare conditionally signaled in the last part of the coding unit level.

TABLE 4 coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth, treeType,modeType ) { ...  LfnstDcOnly = 1  LfnstZeroOutSigCoeffFlag = 1 MtsZeroOutSigCoeffFlag = 1  transform_tree( x0, y0, cbWidth, cbHeight,treeType )  lfnstWidth = ( treeType = = DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC     : ( IntraSubPartitionsSplitType = = ISP_VER_SPLIT) ?cbWidth / NumIntraSubPartitions : cbWidth  lfnstHeight = ( treeType = =DUAL_TREE_CHROMA ) ? cbHeight  / SubHeightC      : (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /NumIntraSubPartitions : cbHeight  if( Min( lfnstWidth, lfnstHeight ) >=4 && sps_lfnst_enabled_flag  = = 1 &&   CuPredMode[ chType ][ x0 ][ y0 ]= = MODE_INTRA &&   ( !intra_mip_flag[ x0 ][ y0 ] | | Min( lfnstWidth,lfnstHeight ) >= 16   ) &&  Max( cbWidth, cbHeight ) <= MaxTbSizeY) {  if( ( IntraSubPartitionsSplitType ! = ISP_NO_SPLIT | |   LfnstDcOnly == 0 ) && LfnstZeroOutSigCoeffFlag = = 1 )    lfnst_idx[ x0 ][ y0 ]  } if( treeType != DUAL_TREE_CHROMA && lfnst_idx[ x0 ][ y0  ] = = 0 &&  transform_skip_flag[ x0 ][ y0 ] = = 0 && Max( cbWidth, cbHeight   ) <=32 &&   IntraSubPartitionsSplit[ x0 ][ y0 ] = = ISP_NO_SPLIT && (  !cu_sbt_flag ) &&   MtsZeroOutSigCoeffFlag = = 1 && tu_cbf_luma[ x0 ][y0 ] ) {   if( ( ( CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTER &&   sps_explicit_mts_inter_enabled_flag )    | | ( CuPredMode[ chType ][x0 ][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ))    mts_idx[ x0 ][ y0 ]  } ...

TABLE 5 transform_unit( x0, y0, tbWidth, tbHeight, treeType, subTuIndex,chType ) { ...  if( tu_cbf_luma[ x0 ][ y0 ] && treeType != DUAL_TREE_CHROMA    && ( tbWidth <= 32 ) && ( tbHeight <= 32 )    && (IntraSubPartitionsSplit[ x0 ][y0 ] = = ISP_NO_SPLIT )    && (!cu_sbt_flag ) ) {   if( sps_transform_skip_enabled_flag && !BdpcmFlag[x0 ][ y0 ]   &&     tbWidth <= MaxTsSize && tbHeight <= MaxTsSize )    transform_skip_flag[ x0 ][ y0 ]  } ...

TABLE 6 residual_coding( x0, y0, log2TbWidth, log2TbHeight, cIdx ) { ... if( ( sps_mts_enabled_flag && cu_sbt_flag && log2TbWidth < 6 &&log2TbHeight < 6 ) )    && cIdx = = 0 && log2TbWidth > 4 )  log2ZoTbWidth = 4  else   log2ZoTbWidth = Min( log2TbWidth, 5 ) MaxCcbs = 2 * ( 1 << log2TbWidth ) * ( 1<< log2TbHeight )  if( (sps_mts_enabled_flag && cu_sbt_flag && log2TbWidth < 6 && log2TbHeight <6 ) )    && cIdx = = 0 && log2TbHeight > 4 )   log2ZoTbHeight = 4  else  log2ZoTbHeight = Min( log2TbHeight, 5 ) ...  if( ( lastSubBlock > 0 &&log2TbWidth >= 2 && log2TbHeight >= 2 )  | |   ( lastScanPos > 7 && (log2TbWidth = = 2 | | log2TbWidth = = 3 )   &&   log2TbWidth = =log2TbHeight ) )   LfnstZeroOutSigCoeffFlag = 0  if( (LastSignificantCoeffX >15 | | LastSignificantCoeffY > 15 ) &&  cIdx = =0 )   MtsZeroOutSigCoeffFlag = 0 ...

The meanings of the main variables in the table are as follows.

1. cbWidth, cbHeight: width and height of the current coding block

2. log 2TbWidth, log 2TbHeight: The log value of base-2 for the widthand height of the current transform block and zero-out are reflected tobe reduced to the upper left area where non-zero coefficients may exist.

3. sps_lfnst_enabled_flag: It is a flag indicating whether the LFNST isenable, if the flag value is 0, it indicates that the LFNST is notenable, and if the flag value is 1, it indicates that the LFNST isenable. It is defined in the Sequence Parameter Set (SPS).

4. CuPredMode[chType][x0][y0]: The prediction mode corresponding to thevariable chType and the (x0, y0) position, chType may have values 0 and1, where 0 represents the luma component and 1 represents the chromacomponent. (x0, y0) position indicates a position on a picture, and MODEINTRA (intra prediction) and MODE INTER (inter prediction) are possiblewith CuPredMode[chType] [x0] [y0] values.

5. IntraSubPartitionsSplit[x0][y0]: The contents of the (x0, y0)position are the same as in No. 4. It is indicated which ISP division atthe (x0, y0) position is applied, and ISP_NO_SPLIT indicates that thecoding unit corresponding to the (x0, y0) position is not divided intopartition blocks.

6. intra_mip_flag[x0][y0]: The contents of the (x0, y0) position are thesame as in No. 4 above. The intra_mip_flag is a flag indicating whethera matrix-based intra prediction (MIP) prediction mode is applied. Theflag value of 0 indicates that MIP is not enable, and the flag value of1 indicates that MIP is applied.

7. cIdx: A value of 0 indicates luma, and values of 1 and 2 indicate Cband Cr, which are chroma components, respectively.

8. treeType: It indicates single-tree and dual-tree, etc. (SINGLE_TREE:single tree, DUAL_TREE_LUMA: dual tree for luma component,DUAL_TREE_CHROMA: dual tree for chroma component)

9. lastSubBlock: It indicates a position in the scan order of asub-block (Coefficient Group (CG)) in which the last non-zerocoefficient is position. 0 indicates a sub-block including a DCcomponent, and if greater than 0, it is not a sub-block including a DCcomponent.

10. lastScanPos: It indicates where the last significant coefficient isin the scan order within one sub-block. If one sub-block consists of 16positions, values from 0 to 15 are possible.

11. lfnst_idx[x0][y0]: LFNST index syntax element to be parsed. If it isnot parsed, it is inferred as a value of 0. That is, the default valueis set to 0 and indicates that LFNST is not applied.

12. LastSignificantCoeffX, LastSignificantCoeffY: It indicates thex-coordinate and y-coordinate where the last significant coefficient islocated in the transform block. The x-coordinate starts at 0 andincreases from left to right, and the y-coordinate starts at 0 andincreases from top to bottom. If the values of both variables are 0, itmeans that the last significant coefficient is located at DC.

13. cu_sbt_flag: It is a flag indicating whether SubBlock Transform(SBT) included in the current VVC standard is enable. If the flag valueis 0, it indicates that SBT is not enable and if the flag value is 1, itindicates that SBT is applied.

14. sps_explicit_mts_inter_enabled_flag,sps_explicit_mts_intra_enabled_flag: It is a flag indicating whether ornot explicit MTS is applied to an inter CU and an intra CU,respectively. If the corresponding flag value is 0, it indicates thatMTS is not applicable to the inter-CU or intra-CU, and if it is 1, itindicates that MTS is applicable.

15. tu_mts_idx[x0][y0]: It is MTS index syntax element to be parsed. Ifit is not parsed, it is inferred as a value of 0. That is, the defaultvalue is set to 0, it is indicated that DCT-2 is applied to both thehorizontal and vertical directions.

As shown in Table 4, several conditions are checked when codingmts_idx[x0][y0], and only when the lfnst_idx[x0][y0] value is 0, tomts_idx[x0][y0] is signaled.

In addition, tu_cbf_luma[x0][y0] is a flag indicating whether asignificant coefficient exists for the luma component. A value of 0indicates that the significant coefficient does not exist in thecorresponding transform block for the luma component, and 1 indicatesthat the significant coefficient exists in the corresponding transformblock for the luma component.

According to Table 4, when both the width and height of the coding unitfor the luma component are 32 or less, mts_idx[x0] [y0] is signaled(Max(cbWidth, cbHeight)<=32), that is, whether or not MTS is applied isdetermined by the width and height of the coding unit for the lumacomponent.

In addition, according to Table 4, even in ISP mode(IntraSubPartitionsSplitType !=ISP_NO_SPLIT) lfnst_idx[x0][y0] may beconfigured to signal, and the same LFNST index value may be applied toall ISP partition blocks.

On the other hand, mts_idx[x0][y0] may be signaled only when not in theISP mode (IntraSubPartitionsSplit[x0][y0]==ISP_NO_SPLIT).

In the process of determining log 2ZoTbWidth and log 2ZoTbHeight asshown in Table 6 (where log 2ZoTbWidth and log 2ZoTbHeight represent thebase-2 log value of the width and height of the upper left arearemaining after zero-out is performed, respectively) the part thatchecks the mts_idx[x0][y0] value may be omitted.

Also, according to an example, a condition for checkingsps_mts_enable_flag may be added when determining log 2ZoTbWidth and log2ZoTbHeight in residual coding.

The variable LfnstZeroOutSigCoeffFlag of Table 4 is 0 if there is asignificant coefficient at the zero-out position when LFNST is applied,otherwise it is 1. The variable UnstZeroOutSigCoeffFlag may be setaccording to several conditions shown in Table 6.

According to an example, the variable LfnstDcOnly in Table 4 becomes 1when all of the last significant coefficients are located at the DCposition (top-left position) for the transform blocks having thecorresponding coded block flag (CBF) (1 if there is at least onesignificant coefficient in the block, 0 otherwise) value of 1, otherwiseit becomes 0. More specifically, in the case of dual tree luma, theposition of the last significant coefficient is checked with respect toone luma transform block, and in the case of dual tree chroma, theposition of the last significant coefficient is checked with respect toboth the transform block for Cb and the transform block for Cr. In thecase of the single tree, the position of the last significantcoefficient may be checked with respect to the transform block for luma,Cb, and Cr.

In Table 4, MtsZeroOutSigCoeffFlag is initially set to 1, and this valuemay be changed in the residual coding of Table 6. The variableMtsZeroOutSigCoeffFlag changes from 1 to 0 if there is a significantcoefficient in the area (LastSignificantCoeffX>15LastSignificantCoeffY>15) that should be filled with 0 due to zero out.In this case, as shown in Table 4, the MTS index is not signaled.

Meanwhile, as shown in Table 4, when tu_cbf_luma[x0][y0] is 0,mts_idx[x0][y0] coding may be omitted. That is, if the CBF value of theluma component is 0, since no transform is applied, there is no need tosignal the MTS index, so the MTS index coding may be omitted.

According to an example, the technical feature may be implemented inanother conditional syntax. For example, after the MTS is performed, itis possible to derive a variable indicating whether a significantcoefficient exists in a region other than the DC region of the currentblock, and if the variable indicates that the significant coefficientexists in a region excluding the DC region, MTS index may be signaled.That is, the existence of a significant coefficient in a region otherthan the DC region of the current block indicates that thetu_cbf_luma[x0][y0] value is 1, and in this case, the MTS index may besignaled.

The variable may be expressed as MtsDcOnly, and after the variableMtsDcOnly is initially set to 1 at the coding unit level, the value maybe changed to 0 when the residual coding level indicates that asignificant coefficient exists in an area other than the DC area of thecurrent block. When the variable MtsDcOnly is 0, the image informationmay be configured such that the MTS index is signaled.

If tu_cbf_luma[x0][y0] is 0, the variable MtsDcOnly maintains an initialvalue of 1 because the residual coding syntax is not called at thetransform unit level of Table 5. In this case, since the variableMtsDcOnly is not changed to 0, the image information may be configuredso that the MTS index is not signaled. That is, the MTS index is notparsed and signaled.

Meanwhile, the decoding apparatus may determine the color index cIdx ofthe transform coefficient to derive the variable MtsZeroOutSigCoeffFlagof Table 6. The color index cIdx of 0 means a luma component.

According to an example, since the MTS may be applied only to the lumacomponent of the current block, the decoding apparatus may determinewhether the color index is luma when deriving the variableMtsZeroOutSigCoeffFlag that determines whether to parse the MTS index.

The variable MtsZeroOutSigCoeffFlag is a variable indicating whetherzero-out is performed when MTS is applied. It indicates whether thetransform coefficient exists in the upper-left region where the lastsignificant coefficient may exist due to zero-out after the MTS isperformed, that is, in the region other than the upper-left 16×16region. The variable MtsZeroOutSigCoeffFlag is initially set to 1 at thecoding unit level as shown in Table 4 (MtsZeroOutSigCoeffFlag=1), and ifthe transform coefficient exists in a region other than the 16×16region, the value changes from 1 to 0 at the residual coding level asshown in Table 6 Can be changed (MtsZeroOutSigCoeffFlag=0). If the valueof the variable MtsZeroOutSigCoeffFlag is 0, the MTS index is notsignaled.

As shown in Table 6, at the residual coding level, the non-zero-outregion in which non-zero transform coefficients may exist may be setdepending on whether or not zero-out accompanying MTS is performed, andeven in this case, when the color index (cIdx) is 0, the non-zero-outarea may be set as the upper left 16×16 region of the current block.

In this way, when deriving a variable for determining whether to parsethe MTS index, it is determined whether the color component is luma orchroma. However, since the LFNST may be applied to both the lumacomponent and the chroma component of the current block, the colorcomponent is not determined when deriving a variable determining whetherto parse the LFNST index.

For example, Table 4 shows a variable LfnstZeroOutSigCoeffFlag that mayindicate that the zero-out is performed when the LFNST is applied. Thevariable UnstZeroOutSigCoeffFlag indicates whether a significantcoefficient exists in the second region except for the first region atthe upper left of the current block. This value is initially set to 1,and if there is a significant coefficient in the second area, the valuemay change to 0. The LFNST index may be parsed only when the value ofthe initially set variable UnstZeroOutSigCoeffFlag is maintained at 1.When determining and deriving whether the variableUnstZeroOutSigCoeffFlag value is 1, since the LFNST may be applied toboth the luma component and the chroma component of the current block,the color index of the current block is not determined.

Meanwhile, the syntax table of the coding unit signaling the LFNST indexaccording to an example is as follows.

TABLE 7 Descriptor coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth,treeType, modeType ) {   ......   LfnstDcOnly = 1  LfnstZeroOutSigCoeffFlag = 1   MtsZeroOutSigCoeffFlag = 1  transform_tree( x0, y0, cbWidth, cbHeight, treeType, chType )  lfnstWidth = ( treeType = = DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC     : ( ( IntraSubPartitionsSplitType = = ISP_VER_SPLIT ) ? cbWidth /      NumIntraSubPartitions : cbWidth )   lfnstHeight = ( treeType = =DUAL_TREE_CHROMA ) ? cbHeight / SubHeightC      : ( (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /      NumIntraSubPartitions : cbHeight )   if( Min( lfnstWidth,lfnstHeight ) >= 4 && sps_lfnst_enabled_flag = = 1 &&    CuPredMode[chType ][ x0 ][ y0 ] = = MODE_INTRA &&    transform_skip_flag[ x0 ][ y0][ 0 ] = = 0 &&    ( treeType = = DUAL_TREE_CHROMA | | !intra_mip_flag[x0 ][ y0 ] | |      Min( lfnstWidth, lfnstHeight ) >= 16 ) &&    Max(cbWidth, cbHeight) <= MaxTbSizeY) {    if( ( IntraSubPartitionsSplitType!= ISP_NO_SPLIT | | LfnstDcOnly = = 0 ) &&     LfnstZeroOutSigCoeffFlag= = 1 )     lfnst_idx ae(v)   }   if( treeType != DUAL_TREE_CHROMA &&lfnst_idx = = 0 &&    transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 && Max(cbWidth, cbHeight ) <= 32 &&    IntraSubPartitionsSplit[ x0 ][ y0 ] = =ISP_NO_SPLIT && cu_sbt_flag = = 0 &&    MtsZeroOutSigCoeffFlag = = 1 &&tu_cbf_luma[ x0 ][ y0 ] ) {    if( ( ( CuPredMode[ chType ][ x0 ][ y0 ]= = MODE_INTER &&     sps_explicit_mts_inter_enabled_flag ) | |     (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )     mts_idx ae(v)   }  }

In Table 7, lfnst_idx means the LFNST index and may have values 0, 1,and 2 as described above. As shown in Table 7, lfnst_idx is signaledonly when the condition (!intra_mip_flag[x0][y0]∥Min(lfnstWidth,lfnstHeight)>=16) is satisfied. Here, intra_mip_flag[x0][y0] is a flagindicating whether or not Matrix-based Intra Prediction (MIP) mode isapplied to the luma block to which the (x0, y0) coordinates belong. Ifthe MIP mode is applied to the luma block, the value is 1, and 0 if notapplied.

lfnstWidth and lfnstHeight indicate the width and height to which LFNSTis applied with respect to a coding block currently being coded(including both a luma coding block and a chroma coding block). When theISP is applied to the coding block, it may indicate the width and heightof each partition block divided into two or four.

In addition, in the above condition, when Min(lfnstWidth,lfnstHeight)>=16 is equal to or greater than a 16×16 block when the MIPis applied (eg, both the width and height of the MIP-applied luma codingblock are equal to or greater than 16), it indicates that the LFNST maybe applied. The meanings of the main variables included in Table 7,which do not overlap with the description of Table 4, are brieflyintroduced as follows.

1. IntraSubPartitionsSplitType: It indicates how the ISP partition isformed for the current coding unit, and ISP_NO_SPLIT means that thecorresponding coding unit is not a coding unit split into partitionblocks. ISP_VER_SPLIT indicates vertical split, and ISP_HOR_SPLITindicates horizontal split. For example, when a W×H (width W, height H)block is horizontally split into n partition blocks, it is split intoW×(H/n) blocks, and when a W×H (width W, height H) block is verticallysplit into n partition blocks, it is split into (W/n)×H blocks.

2. SubWidthC, SubHeightC: SubWidthC and SubHeightC are values setaccording to a color format (or a chroma format, for example 4:2:0,4:2:2, 4:4:4), and more specifically, it indicates the ratio of thewidth and the height of the luma component and the chroma component,respectively. (See table below)

TABLE 8 Chroma format SubWidthC SubHeightC Monochrome 1 1 4:2:0 2 24:2:2 2 1 4:4:4 1 1 4:4:4 1 1

3. NumIntraSubPartitions: It indicates how many partition blocks aredivided when the ISP is applied. That is, it indicates that thepartition is divided into NumIntraSubPartitions partition blocks.

4. LfnstDcOnly: For all transform blocks belonging to the current codingunit, each last non-zero coefficient position is a DC position (ie, atop-left position within the corresponding transform block) or when asignificant coefficient does not exist (that is, when the correspondingCBF value is 0), the value of the LnfstDCOnly variable becomes 1.

In the case of the luma separate-tree or the luma dual-tree, theLfnstDcOnly variable value is determined by checking the condition onlyfor transform blocks corresponding to the luma component in thecorresponding coding unit, and in the case of the chroma separate-treeor the chroma dual-tree, the LfnstDcOnly variable value may bedetermined by checking the condition only for transform blockscorresponding to the chroma components (Cb, Cr) in the correspondingcoding unit In the case of the single tree, the LfnstDcOnly variablevalue may be determined by checking the above conditions for alltransform blocks corresponding to the luma component and the chromacomponent (Cb, Cr) in the corresponding coding unit.

5. LfnstZeroOutSigCoeffFlag: When the LFNST is applied, it is set to 1if the significant coefficient exists only in the region where thesignificant coefficient may exist; otherwise, it is set to 0.

In the case of the 4×4 transform block or the 8×8 transform block, up to8 significant coefficients may be located from the (0, 0) position(top-left) in the corresponding transform block according to thescanning order, and for the remaining positions in the correspondingtransform block, are zeroed out. In the case of a transform block thatis not 4×4 and 8×8 and whose width and height are equal to or greaterthan 4, respectively (that is, a transform block to which the LFNST maybe applied), according to the scanning order, 16 significantcoefficients can be located from the (0, 0) position (top-left) in thecorresponding transform block (that is, the significant coefficient canbe located only within the upper left 4×4 block) and is zeroed out forthe remaining positions in the corresponding transform block.

In addition, as shown in Table 7, when coded in a split tree or a dualtree, whether the MIP is applied to the chroma component is not checkedwhen signaling the LFNST index. Through this, the LFNST may be properlyapplied to the chroma component.

As shown in Table 7, when the condition (treeType==DUAL_TREE_CHROMA∥!intra_mip_flag[x0][y0]∥ Min(lfnstWidth, lfnstHeight)>=16)))) issatisfied, the LFNST index is signaled. This means that (Min(lfnstWidth,lfnstHeight)>=16)) LFNST index is signaled when the tree type is a dualtree chroma type (treeType==DUAL_TREE_CHROMA), MIP mode not applied(!intra_mip_flag[x0][y0]), or the smaller of the width and height of theblock to which LFNST is applied is 16 or more. That is, when the codingblock is the dual tree chroma, the LFNST index is signaled withoutdetermining whether the MIP mode is applied or the width and height ofthe block to which the LFNST is applied.

In addition, the above condition can be interpreted as that if thecoding block is not dual tree chroma and MIP is not applied, the LFNSTindex is signaled without determining the width and height of the blockto which the LFNST is applied.

In addition, when the coding block is not the dual tree chroma and theMIP is applied, it may be interpreted that the LFNST index may besignaled when the smaller of the width and the height of the block towhich the LFNST is applied is 16 or more.

On the other hand, only when transform skip is not applied to the lumacomponent as shown in Table 7 (that is, when the conditiontransform_skip_flag[x0] [y0][0]==0 is satisfied), the LFNST index issignaled.

Here, x0 and y0 mean (x0, y0) coordinates when the upper-left positionis (0, 0) in the picture for the luma component, and the horizontal Xcoordinate increases from left to right, and the vertical Y coordinateincreases from top to bottom.

(x0, y0) is a coordinate based on the luma component, but may also beused for the chroma phase component. In this case, the actual positionindicated by the (x0, y0) coordinate may be scaled based on the picturefor the chroma component. For example, when the chroma format is 4:2:0,the actual position of the chroma component indicated by (x0, y0) on thepicture may be (x0/2, y0/2). For example, when the chroma format is4:2:0, the actual position of the chroma component indicated by (x0, y0)on the picture may be (x0/2, y0/2).

In transform_skip_flag[x0][y0][0], the last index 0 refers to the lumacomponent. More specifically, in transform_skip_flag[x0][y0][cIdx], cIdxrefers to which component it is for, and if the cIdx value is 0, a cIdxvalue of 0 indicates luma, and cIdx greater than 0 (1 or 2) indicateschroma.

In addition, the variable LfnstDcOnly is initialized to a value of 1 asshown in Table 7, and may be set to a value of 0 according to acondition in the parsing function for residual coding as shown in thetable below.

TABLE 9 Descriptor residual_coding( x0, y0, log2TbWidth, log2TbHeight,cIdx ) {  if( sps_mts_enabled_flag && cu_sbt_flag && cIdx = = 0 &&   log2TbWidth < 6 && log2TbHeight < 6 && log2TbWidth > 4 )  log2ZoTbWidth = 4  else   log2ZoTbWidth = Min( log2TbWidth, 5 )  if(sps_mts_enabled_flag && cu_sbt_flag && cIdx = = 0 &&    log2TbWidth < 6&& log2TbHeight < 6 && log2TbHeight > 4 )   log2ZoTbHeight = 4  else  log2ZoTbHeight = Min( log2TbHeight, 5 )  if( log2TbWidth > 0 )  last_sig_coeff_x_prefix ae(v)  if( log2TbHeight > 0 )  last_sig_coeff_y_prefix ae(v)  if( last_sig_coeff_x_prefix > 3 )  last_sig_coeff_x_suffix ae(v)  if( last_sig_coeff_y_prefix > 3 )  last_sig_coeff_y_suffix ae(v)  log2TbWidth = log2ZoTb Width log2TbHeight = log2ZoTbHeight  remBinsPass1 = ( ( 1 << ( log2TbWidth +log2TbHeight ) ) * 7 ) >> 2  log2SbW = ( Min( log2TbWidth, log2TbHeight) < 2 ? 1 : 2 )  log2SbH = log2SbW  if( log2TbWidth + log2TbHeight > 3 ){   if( log2TbWidth < 2 ) {    log2SbW = log2TbWidth    log2SbH = 4 −log2SbW   } else if( log2TbHeight < 2 ) {    log2SbH = log2TbHeight   log2SbW = 4 − log2SbH   }  }  numSbCoeff = 1 << ( log2SbW + log2SbH ) lastScanPos = numSbCoeff  lastSubBlock = ( 1 << ( log2TbWidth +log2TbHeight − ( log2SbW + log2SbH ) ) ) − 1  do {   if( lastScanPos = =0 ) {    lastScanPos = numSbCoeff    lastSubBlock− −   }   lastScanPos−−   xS = DiagScanOrder[ log2TbWidth − log2SbW ][ log2TbHeight − log2SbH]      [ lastSubBlock ][ 0 ]   yS = DiagScanOrder[ log2TbWidth − log2SbW][ log2TbHeight − log2SbH ]      [ lastSubBlock ][ 1 ]   xC = ( xS <<log2SbW ) + DiagScanOrder[ log2SbW ][ log2SbH ][ lastScanPos ][ 0 ]   yC= ( yS << log2SbH ) + DiagScanOrder[ log2SbW ][ log2SbH ][lastScanPos ][1 ]  } while( ( xC != LastSignificantCoeffX ) | | ( yC !=LastSignificantCoeffY ) )  if( lastSubBlock = = 0 && log2TbWidth >= 2 &&log2TbHeight >= 2 &&   !transform_skip_flag[ x0 ][ y0 ][ cIdx ] &&lastScanPos > 0 )   LfnstDcOnly = 0  if( ( lastSubBlock > 0 &&log2TbWidth >= 2 && log2TbHeight >= 2 ) | |   ( lastScanPos > 7 && (log2TbWidth = = 2 | | log2TbWidth = = 3 ) &&   log2TbWidth = =log2TbHeight ) )   LfnstZeroOutSigCoeffFlag = 0  ...... }

As shown in Table 9, the LfnstDcOnly value may be set to 0 only when thetransform_skip_flag[x0][y0][cIdx] value is 0 (that is, only whentransform skip is not applied to the component indicated by cIdx). If itis not in the ISP mode, as shown in Table 7, the LFNST index is signaledonly when the LfnstDcOnly value is 0, and the LFNST index value may beinferred to be 0 when the LFNST index is not signaled.

For reference, the residual coding function presented in Table 9 iscalled while performing the transform tree called in Table 7, and forthe single tree, the residual coding function for luma (cIdx=0) andchroma (cIdx=1 or 2, corresponding to the Cb component and Cr component)are all called, and for the dual tree, only the residual coding functionfor luma (cIdx=0) is called in the case of the dual tree for luma(DUAL_TREE_LUMA) and only the residual coding function for chroma(cIdx=1 or 2, corresponding to Cb and Cr components) is called in thecase of the dual tree for chroma (DUAL_TREE_CHROMA).

The conditions under which the LFNST index is signaled for the case ofnot in the ISP mode are summarized as follows (here, it can be assumedthat other conditions for the LFNST index to be signaled are satisfied,for example, the condition Max(cbWidth, cbHeight)<=MaxTbSizeY is assumedto be satisfied).

1. When transform_skip_flag[x0][y0][0] is 1

-   -   LFNST index is inferred as 0 without signaling

2. When transform_skip_flag[x0][y0][0] is 0

2-A. When transform_skip_flag[x0] [y0][1] is 0 andtransform_skip_flag[x0] [y0][2] is 0

-   -   LfnstDcOnly value can be set to 0 for all cIdx in Table 9 (for        cIdx 0, 1, 2)    -   If the LfnstDcOnly value is 0, the LFNST index is signaled;        otherwise, the LFNST index is not signaled and the value is        inferred as 0.

2-B. When transform_skip_flag[x0] [y0][1] is 0 andtransform_skip_flag[x0] [y0][2] is 1

-   -   In Table 9, the LfnstDcOnly value can be set to 0 only when cIdx        is 0 and 1    -   If the LfnstDcOnly value is 0, the LFNST index is signaled;        otherwise, the LFNST index is not signaled and the value is        inferred as 0.

2-C. When transform_skip_flag[x0] [y0][1] is 1 andtransform_skip_flag[x0] [y0][2] is 0

-   -   In Table 9, the LfnstDcOnly value can be set to 0 only when cIdx        is 0 and 2    -   If the LfnstDcOnly value is 0, the LFNST index is signaled;        otherwise, the LFNST index is not signaled and the value is        inferred to be 0.

2-D. When transform_skip_flag[x0] [y0][1] is 1 andtransform_skip_flag[x0][y0][2] is 1

-   -   In Table 9, the LfnstDcOnly value can be set to 0 only when cIdx        is 0        -   If the LfnstDcOnly value is 0, the LFNST index is signaled;            otherwise, the LFNST index is not signaled and the value is            inferred as 0.

In the case of the single tree, transform_skip_flag[x0][y0][0],transform_skip_flag[x0][y0][1], transform_skip_flag[x0][y0][2] valuesare checked for the above cases, in the case of the dual tree for luma,only transform_skip_flag[x0][y0][0] is checked, and in the case of adual tree for chroma, the values of transform_skip_flag[x0][y0][1] andtransform_skip_flag[x0][y0][2] are checked.

In the case of the ISP mode (IntraSubPartitionsSplitType !=ISP_NO_SPLITcondition in Table 7, that is, horizontal division or verticaldivision), as shown in Table 7, the LfnstDcOnly variable is not checkedand the LFNST index is signaled.

Therefore, in the case of the ISP mode in the single tree and dual treefor luma, regardless of the value of LfnstDcOnly variable, whentransform_skip_flag[x0][y0][0] value is 0 (transform skip is not appliedfor luma component), the LFNST index is signaled (when the LFNST indexis not signaled, the LFNST index value may be inferred to be 0).

In the case of the dual tree for chroma, based on the fact that ISPprediction is applied only to luma in the current VVC standard, it isconsidered that ISP is not applied to the chroma, and the LFNST indexmay be signaled by checking the LfnstDcOnly variable as in the abovemethod, and as shown in Table 9, the LfnstDcOnly variable may be set to0 only when the transform_skip_flag[x0][y0][cIdx] value is 0.

Of course, application of ISP mode to luma affects even a dual tree forchroma, so even in the case of the dual tree for chroma, the LFNST indexmay be signaled when the transform_skip_flag[x0][y0][0] value is 0regardless of the LfnstDcOnly variable.

The conditions under which the LFNST index is signaled when the ISP modeis applied and the transform_skip_flag[x0][y0][0] value is 0 aresummarized as follows. If the transform_skip_flag[x0][y0][0] value is 1,the LFNST index is not signaled and is inferred to be 0. Of course, itcan be assumed that other conditions necessary for signaling the LFNSTindex in Table 7 are satisfied, for example, it can be assumed that acondition such as Max(cbWidth, cbHeight)<=MaxTbSizeY is satisfied.

1. In the case of the single tree

-   -   LFNST index signaling regardless of the LfnstDcOnly variable        value

2. In the case of the dual tree

2-A. In the case of the duel tree for luma

-   -   LFNST index signaling regardless of the LfnstDcOnly variable        value

2-B. In the case of the dual tree for chroma

-   -   According to the values of transform_skip_flag[x0][y0][1] and        transform_skip_flag[x0][y0][2], when the LfnstDcOnly variable        value is set to 0, that is, the cIdx value in        transform_skip_flag[x0][y0][cIdx] is 1, LfnstDcOnly variable        value may be set to 0 only when transform_skip_flag[x0][y0][1]        value is 0 and when the cIdx value is 2, the LfnstDcOnly        variable value can be set to 0 only when the        transform_skip_flag[x0][y0][2] value is 0.    -   If the LfnstDcOnly value is 0, the LFNST index is signaled;        otherwise, the LFNST index is not signaled and the value is        inferred to be 0.

In the above cases, the case of the dual tree for chroma is the same asthe case where the ISP is not applied.

Meanwhile, according to an example, while the transform skip for achroma component is permitted in the current VVC standard, a transformskip flag corresponding to each chroma component is added as shown inthe table below.

TABLE 10 Descriptor transform_unit( x0, y0, tbWidth, tbHeight, treeType,subTuIndex, chType ) {   ......  if( tu_cbf_luma[ x0 ][ y0 ] && treeType!= DUAL_TREE_CHROMA ) {   if( sps_transform_skip_enabled_flag &&!BdpcmFlag[ x0 ][ y0 ][ 0 ] &&..    tbWidth <= MaxTsSize && tbHeight <=MaxTsSize &&    ( IntraSubPartitionsSplit[ x0 ][ y0 ] = = ISP_NO_SPLIT )&& !cu_sbt_flag )    transform_skip_flag[ x0 ][ y0 ][ 0 ] ae(v)   if(!transform_skip_flag[ x0 ][ y0 ][ 0 ] )    residual_coding( x0, y0,Log2( tbWidth ), Log2( tbHeight ), 0 )   else    residual_ts_coding( x0,y0, Log2( tbWidth), Log2( tbHeight), 0 )  }  if( tu_cbf_cb[ xC ][ yC ]&& treeType != DUAL_TREE_LUMA ) {   if( sps_transform_skip_enabled_flag&& !BdpcmFlag[ x0 ][ y0 ][ 1 ] &&    wC <= MaxTsSize && hC <= MaxTsSize&& !cu_sbt_flag )    transform_skip_flag[ xC ][ yC ][ 1 ] ae(v)   if(!transform_skip_flag[ xC ][ yC ][ 1 ] )    residual_coding( xC, yC,Log2( wC ), Log2( hC ), 1 )   else    residual_ts_coding( xC, yC, Log2(wC ), Log2( hC), 1 )  }  if( tu_cbf_cr[ xC ][ yC ] && treeType !=DUAL_TREE_LUMA &&   !( tu_cbf_cb[ xC ][ yC ] &&tu_joint_cbcr_residual_flag[ xC ][ yC ] ) ) {   if(sps_transform_skip_enabled_flag && !BdpcmFlag[ x0 ][ y0 ][ 2 ] &&    wC<= MaxTsSize && hC <= MaxTsSize && !cu_sbt_flag )   transform_skip_flag[ xC ][ yC ][ 2 ] ae(v)   if(!transform_skip_flag[ xC ][ yC ][ 2 ] )    residual_coding( xC, yC,Log2( wC ), Log2( hC ), 2 )   else    residual_ts_coding( xC, yC, Log2(wC), Log2( hC), 2 )  } }

In Table 10, except for the case of the dual tree for luma, it can beconfirmed that transform_skip_flag[xC][yC][1] corresponding to whetherthe transform skip is applied to Cb and transform_skip_flag[xC][yC][2]corresponding to whether transform skip is applied to Cr may besignaled. If transform_skip_flag[xC][yC][1] value is 1, the transformskip is applied to Cb, and if it is 0, the transform skip is not appliedto Cb, and if transform_skip_flag[xC][yC][2] value is 1, the transformskip is applied to Cr, and if it is 0, the transform skip is not appliedto Cr.

Therefore, even when the LFNST index value is greater than 0 (that is,when LFNST is applied), each transform_skip_flag[x0][y0][cIdx] value forthe luma component (Y component) and the chroma component (Cb componentand Cr component) may be different. According to Table 7, since theLFNST index value may be greater than 0 only when thetransform_skip_flag[x0][y0][0] value is 0, when the LFNST index value isgreater than 0, transform_skip_flag[x0][y0][0] is always zero.

Accordingly, the cases in which the LFNST may be applied according tothe transform_skip_flag[x0][y0][cIdx] value are summarized as follows.Here, the LFNST index is greater than 0 and thetransform_skip_flag[x0][y0][0] value is 0. It may be assumed that otherconditions for applying the LFNST are satisfied, for example, both thewidth and height of the corresponding block may be greater than or equalto 4.

1. Single tree

-   -   Apply LFNST to luma component    -   If a transform_skip_flag[x0][y0][1] value is 0, the LFNST is        applied to the Cb component, and if it is 1, the LFNST is not        applied to the Cb component.    -   If a transform_skip_flag[x0][y0][2] value is 0, the LFNST is        applied to the Cr component, and if it is 1, the LFNST is not        applied to the Cr component.

2. Duel tree for luma

-   -   Apply LFNST to luma component

3. Duel tree for chroma

-   -   If the transform_skip_flag[x0][y0][1] value is 0, the LFNST is        applied to the Cb component, and if it is 1, the LFNST is not        applied to the Cb component.    -   If the transform_skip_flag[x0][y0][2] value is 0, the LFNST is        applied to the Cr component, and if it is 1, the LFNST is not        applied to the Cr component.

As described above, to selectively apply the LFNST according to thetransform_skip_flag[x0][y0][cIdx] value, the following conditions shouldbe added to the specification text for the LFNST.

TABLE 11 8.7.4  Transformation process for scaled transform coefficients8.7.4.1  General Inputs to this process are: - a luma location ( xTbY,yTbY ) specifying the top-left sample of the current luma transformblock relative   to the top-left luma sample of the current picture, - avariable nTbW specifying the width of the current transform block, - avariable nTbH specifying the height of the current transform block, - avariable cIdx specifying the colour component of the current block, - an(nTbW)x(nTbH) array d[ x ][ y ] of scaled transform coefficients with x= 0..nTbW − 1,   y = 0..nTbH − 1. Output of this process is the(nTbW)x(nTbH) array res[ x ][ y ] of residual samples with x = 0..nTbW −1, y = 0..nTbH − 1. When lfnst_idx is not equal to 0 andtransform_skip_flag[ xTbY ][ yTbY ][ cIdx ] is equal to 0 and both nTbWand nTbH are greater than or equal to 4, the following applies: - Thevariables predModeIntra, nLfnstOutSize, log2LfnstSize, nLfnstSize, andnonZeroSize are derived as   follows:   predModeIntra =   ( cIdx = = 0 )? IntraPredModeY[ xTbY ][ yTbY ] : IntraPredModeC[ xTbY ][ yTbY ] (  8-954)   nLfnstOutSize = ( nTbW >= 8 && nTbH >= 8 ) ? 48 : 16 (8-955)  log2LfnstSize = ( nTbW >= 8 && nTbH >= 8 ) ? 3 : 2 (8-956)  nLfnstSize =   1 << log2LfnstSize (8-957)   nonZeroSize = ( ( nTbW = =4 && nTbH = = 4 ) | |   ( nTbW = = 8 && nTbH = = 8 ) ) ? 8 : 16 (8-958)- When intra_mip_flag[ xTbY ][ yTbY ] is equal to 1 and cIdx is equal to0, predModeIntra is set equal to   INTRA_PLANAR. - When predModeIntra isequal to either INTRA_LT_CCLM, INTRA_L_CCLM, or INTRA_T_CCLM,  predModeIntra is derived as follows:  - If intra_mip_flag[ xTbY + nTbW *SubWidthC / 2 ][ yTbY + nTbH * SubHeightC / 2 ] is equal to 1,   predModeIntra is set equal to INTRA_PLANAR.  - Otherwise,    CuPredMode[0 ][ xTbY + nTbW * SubWidthC / 2 ][ yTbY + nTbH * SubHeightC / 2 ] isequal to    MODE_IBC or MODE_PLT, predModeIntra is set equal toINTRA_DC.  - Otherwise, predModeIntra is set equal to    IntraPredModeY[xTbY + nTbW * SubWidthC / 2 ][ yTbY + nTbH * SubHeightC / 2 ]. - Thewide angle intra prediction mode mapping process as specified in clause8.4.5.2.6 is invoked with   predModeIntra, nTbW, nTbH and cIdx asinputs, and the modified predModeIntra as output. - The values of thelist u[ x ] with x = 0..nonZeroSize − 1 are derived as follows:   xC =  DiagScanOrder[ 2 ][ 2 ][ x ][ 0 ] (8-959)   yC =   DiagScanOrder[ 2 ][2 ][ x ][ 1 ] (8-960)   u[ x ] = d[ xC ][ yC ] (8-961) - Theone-dimensional low frequency non-separable transformation process asspecified in clause 8.7.4.2 is  invoked with the input length of thescaled transform coefficients nonZeroSize, the transform output length nTrS set equal to nLfnstOutSize, the list of scaled non-zero transformcoefficients u[ x ] with  x = 0..nonZeroSize − 1, and the intraprediction mode for LFNST set selection predModeIntra as inputs,  andthe list v[ x ] with x = 0..nLfnstOutSize − 1 as output. - The array d[x ][ y ] with x = 0..nLfnstSize − 1, y = 0..nLfnstSize − 1 is derived asfollows:  - If predModeIntra is less than or equal to 34, the followingapplies:   d[ x ][ y ] = ( y < 4 ) ? v[ x + ( y << log2LfnstSize ) ] :(8-962)    ( ( x < 4 ) ? v[ 32 + x + ( ( y − 4 ) << 2 ) ] : d[ x ][ y ])  - Otherwise, the following applies:   d[ x ][ y ] = ( x < 4 ) ? v[y + ( x << log2LfnstSize ) ] : (8-963)    ( ( y < 4 ) ? v[ 32 + y + ( (x − 4 ) << 2 ) ] : d[ x ][ y ] ) ......

As shown in Table 11, when the LFNST index (lfnst_idx) value is not 0(that is, when LFNST is applied), by checking thetransform_skip_flag[xTbY][yTbY][cIdx] value for the component specifiedby cIdx (When lfnst_idx is not equal to 0 andtransform_skip_flag[xTbY][yTbY][cIdx] is equal to 0 and both nTbW andnTbH are greater than or equal to 4, the following applies), it may beconfigured such that the subsequent coding process is performed onlywhen the transform_skip_flag[xTbY][yTbY][cIdx] value is 0, that is,LFNST is applied.

Meanwhile, the LFNST index may be signaled according to whether thetransform is skipped for each color component.

As an example, when compared with Table 7, in Table 12, the conditionfor transmitting the LFNST index can be removed only when thetransform_skip_flag[x0][y0][0] value is 0

TABLE 12 Descriptor coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth,treeType, modeType ) {   ......   LfnstDcOnly = 1  LfnstZeroOutSigCoeffFlag = 1   MtsZeroOutSigCoeffFlag = 1  transform_tree( x0, y0, cbWidth, cbHeight, treeType, chType )  lfnstWidth = ( treeType = = DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC     : ( ( IntraSubPartitionsSplitType = = ISP_VER_SPLIT ) ? cbWidth /      NumIntraSubPartitions : cbWidth )   lfnstHeight = ( treeType = =DUAL_TREE_CHROMA ) ? cbHeight / SubHeightC      : ( (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /      NumIntraSubPartitions : cbHeight )   if( Min( lfnstWidth,lfnstHeight ) >= 4 && sps_lfnst_enabled_flag = = 1 &&    CuPredMode[chType ][ x0 ][ y0 ] = = MODE_INTRA &&    ( treeType = =DUAL_TREE_CHROMA | | !intra_mip_flag[ x0 ][ y0 ] | |      Min(lfnstWidth, lfnstHeight ) >= 16 ) &&    Max( cbWidth, cbHeight ) <=MaxTbSizeY) {    if( ( IntraSubPartitionsSplitType != ISP_NO_SPLIT | |LfnstDcOnly = = 0 ) &&     LfnstZeroOutSigCoeffFlag = = 1 )    lfnst_idx ae(v)   }   if( treeType != DUAL_TREE_CHROMA && lfnst_idx= = 0 &&    transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 && Max( cbWidth,cbHeight ) <= 32 &&    IntraSubPartitionsSplit[ x0 ][y0 ] = =ISP_NO_SPLIT && cu_sbt_flag = = 0 &&    MtsZeroOutSigCoeffFlag = = 1 &&tu_cbf_luma[ x0 ][ y0 ] ) {    if( ( ( CuPredMode[ chType ][ x0 ][ y0 ]= = MODE_INTER &&     sps_explicit_mts_inter_enabled_flag ) | |     (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )     mts_idx ae(v)   }  }

However, since the method of setting the LfnstDcOnly variable valuedescribed in Table 12 is the same as in Table 9, the setting of theLfnstDcOnly variable value changes according to thetransform_skip_flag[x0][y0][cIdx] value, and finally whether the LFNSTindex is signaled will also change.

When the ISP mode is not applied, how the LFNST index is signaled by thetransform_skip_flag[x0][y0][cIdx] value is summarized as follows. It maybe assumed that other conditions for signaling the LFNST index arealready satisfied, for example, a condition such as Max(cbWidth,cbHeight)<=MaxTbSizeY is satisfied.

1. In case of single tree

-   -   When the transform_skip_flag[x0][y0][0] value is 0, the        LfnstDcOnly variable value may be set to 0 according to the        method shown in Table 9.    -   When the transform_skip_flag[x0][y0][1] value is 0, the        LfnstDcOnly variable value may be set to 0 according to the        method shown in Table 9.    -   When the transform_skip_flag[x0][y0][2] value is 0, the        LfnstDcOnly variable value may be set to 0 according to the        method shown in Table 9.    -   When the LfnstDcOnly value is 0, the LFNST index may be        signaled. If the LFNST index is not signaled, it may be inferred        to be 0.

2. In case of dual tree for luma component

-   -   When the transform_skip_flag[x0][y0][0] value is 0, the        LfnstDcOnly variable value may be set to 0 according to the        method shown in Table 9.    -   When the LfnstDcOnly value is 0, the LFNST index may be        signaled. If the LFNST index is not signaled, it may be inferred        to be 0.

3. In case of dual tree for chroma component

-   -   When the transform_skip_flag[x0][y0][1] value is 0, the        LfnstDcOnly variable value may be set to 0 according to the        method shown in Table 9.    -   When the transform_skip_flag[x0][y0][2] value is 0, the        LfnstDcOnly variable value may be set to 0 according to the        method shown in Table 9.    -   When the LfnstDcOnly value is 0, the LFNST index may be        signaled. If the LFNST index is not signaled, it may be inferred        to be 0.

As shown in Table 12, the LfnstDcOnly value is initialized to 1, and inthe case of the dual tree, the LFNST index corresponding to the dualtree for luma and the LFNST index corresponding to the dual tree forchroma may be separately signaled. This means that different LFNSTkernels may be applied to luma and chroma.

In addition, the dual tree shown in Tables 7 to 12 may includeDUAL_TREE_LUMA (corresponding to a luma component) and DUAL_TREE_CHROMA(corresponding to a chroma component) appearing on the current VVCspecification document, which may include a case in which a syntaxparsing tree for luma and a syntax parsing tree for chroma aredifferentiated due to a size condition of a coding unit or the like. Forexample, the case of a separate tree may be included.

When the ISP mode is applied, transform_skip_flag[x0][y0] [0] is notsignaled and is inferred to be 0 as shown in Table 10. That is, as shownin Table 10, transform_skip_flag[x0][y0][0] is signaled only when thecondition IntraSubPartitionsSplit[x0] [y0]==ISP_NO_SPLIT, which is thecase where the ISP mode is not applied, is satisfied.

In addition, as shown in Table 10, transform_skip_flag[x0][y0][1] andtransform_skip_flag[x0][y0][2] may be signaled regardless of whether theISP mode is applied.

Therefore, the LFNST signaling for the case where the ISP mode isapplied may be summarized as follows. It may be assumed that otherconditions for signaling the LFNST index are already satisfied, forexample, a condition such as Max(cbWidth, cbHeight)<=MaxTbSizeY may besatisfied.

1. In case of single tree

-   -   LFNST index may be signaled. If the LFNST index is not signaled,        it may be inferred to be 0.

2. In case of dual tree for luma component

-   -   LFNST index may be signaled. If the LFNST index is not signaled,        it may be inferred to be 0.

3. In case of dual tree for chroma component

-   -   When the transform_skip_flag[x0][y0][1] value is 0, the        LfnstDcOnly variable value may be set to 0 according to the        method shown in Table 9.    -   When the transform_skip_flag[x0] [y0][2] value is 0, the        LfnstDcOnly variable value may be set to 0 according to the        method shown in Table 9.    -   When the LfnstDcOnly value is 0, the LFNST index may be        signaled. If the LFNST index is not signaled, it may be inferred        to be 0.

When the ISP mode is applied, the LfnstDcOnly condition is not checkedas shown in Table 12. Therefore, in the case of the first single treeand the dual tree for the second luma component, the LFNST index may besignaled without checking the LfnstDcOnly condition. In the case of thedual tree for chroma, the LFNST index may be signaled according to thesame conditions as in the case where the ISP mode is not applied as incase 3 above. That is, the LFNST index is signaled according to theLfnstDcOnly condition.

According to an example, since transform_skip_flag[x0][y0][cIdx] valuesmay be assigned to the luma component and the two chroma components,respectively, when the LFNST index value is greater than 0, that is,even when the LFNST is applied, only when thetransform_skip_flag[x0][y0] [cIdx] value is 0, the LFNST may be appliedto the component indicated by cIdx. The contents of the specificationtext changed correspondingly are the same as in Table 11.

According to an example, if the condition for checking whether thetransform_skip_flag[x0][y0][0] value is 0 only for the dual tree casecompared to Table 7 is removed, the LFNST index signaling may beconfigured as shown in Table 13. The LfnstDcOnly variable shown in Table13 may be set to 0 according to conditions as shown in Table 9.

TABLE 13 Descriptor coding_unit( x0, y0, cbWidth, cbHeight, cqtDepth,treeType, modeType ) {   ......   LfnstDcOnly = 1  LfnstZeroOutSigCoeffFlag = 1   MtsZeroOutSigCoeffFlag = 1  transform_tree( x0, y0, cbWidth, cbHeight, treeType, chType )  lfnstWidth = ( treeType = = DUAL_TREE_CHROMA ) ? cbWidth / SubWidthC     : ( ( IntraSubPartitionsSplitType = = ISP_VER_SPLIT ) ? cbWidth /      NumIntraSubPartitions : cbWidth )   lfnstHeight = ( treeType = =DUAL_TREE_CHROMA ) ? cbHeight / SubHeightC      : ( (IntraSubPartitionsSplitType = = ISP_HOR_SPLIT) ? cbHeight /      NumIntraSubPartitions : cbHeight )   if( Min( lfnstWidth,lfnstHeight ) >= 4 && sps_lfnst_enabled_flag = = 1 &&    CuPredMode[chType ][ x0 ][ y0 ] = = MODE_INTRA &&    ( treeType != SINGLE_TREE | |transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 ) &&    ( treeType = =DUAL_TREE_CHROMA | | !intra_mip_flag[ x0 ][ y0 ] | |      Min(lfnstWidth, lfnstHeight ) >= 16 ) &&    Max( cbWidth, cbHeight ) <=MaxTbSizeY) {    if( ( IntraSubPartitionsSplitType != ISP_NO_SPLIT | |LfnstDcOnly = = 0 ) &&     LfnstZeroOutSigCoeffFlag = = 1 )    lfnst_idx ae(v)   }   if( treeType != DUAL_TREE_CHROMA && lfnst_idx= = 0 &&    transform_skip_flag[ x0 ][ y0 ][ 0 ] = = 0 && Max( cbWidth,cbHeight ) <= 32 &&    IntraSubPartitionsSplit[ x0 ][ y0 ] = =ISP_NO_SPLIT && cu_sbt_flag = = 0 &&    MtsZeroOutSigCoeffFlag = = 1 &&tu_cbf_luma[ x0 ][ y0 ] ) {    if( ( ( CuPredMode[ chType ][ x0 ][ y0 ]= = MODE_INTER &&     sps_explicit_mts_inter_enabled_flag ) | |     (CuPredMode[ chType ][ x0 ][ y0 ] = = MODE_INTRA &&    sps_explicit_mts_intra_enabled_flag ) ) )     mts_idx ae(v)   }  }

When configured as shown in Table 13, in the case of the single tree,the LFNST index signaling method shown in Tables 7 to 9 may be applied,and in the case of the dual tree, the method shown in Table 12 may beapplied. In addition, since the transform_skip_flag[x0][y0][cIdx] valuesare assigned to the luma component and the two chroma components,respectively, as shown in Tables 7 to 9, even if the LFNST index valueis greater than 0 (i.e. when LFNST is applied), it may be configured toapply LFNST to the component indicated by cIdx only when thetransform_skip_flag[x0][y0][cIdx] value is 0. The contents of thespecification text changed correspondingly are the same as in Table 11.

The following drawings were created to explain a specific example of thepresent specification. Since the names of specific devices described inthe drawings or the names of specific signals/messages/fields arepresented by way of example, the technical features of the presentspecification are not limited to the specific names used in thefollowing drawings.

FIG. 15 is a flowchart illustrating an operation of a video decodingapparatus according to an embodiment of the present disclosure.

Each step disclosed in FIG. 15 is based on some of the contentsdescribed above in FIGS. 5 to 4 . Accordingly, detailed descriptionsoverlapping with those described above in FIGS. 3 and 5 to 14 will beomitted or simplified.

The decoding apparatus 300 according to an embodiment may receiveinformation on an intra prediction mode, residual information, and anLFNST index from a bitstream (S1510).

More specifically, the decoding apparatus 300 may decode information onthe quantized transform coefficients for the current block from thebitstream, and derive quantized transform coefficients for the targetblock based on information on the quantized transform coefficients forthe current block. The information on the quantized transformcoefficients for the target block may be included in a sequenceparameter set (SPS) or a slice header, and may include at least one ofinformation on the simplification factor, information on the minimumtransform size to apply a simplified transform, information on themaximum transform size to apply a simplified transform, and informationon a transform index indicating any one of a simplified inversetransform size and a transform kernel matrix included in a transform set

In addition, the decoding apparatus may further receive information onan intra prediction mode for the current block and information onwhether the ISP is applied to the current block. The decoding apparatusmay derive whether the current block is divided into a predeterminednumber of sub-partition transform blocks by receiving and parsing flaginformation indicating whether to apply ISP coding or ISP mode. Here,the current block may be a coding block. Also, the decoding apparatusmay derive the size and number of divided sub-partition blocks throughflag information indicating in which direction the current block is tobe divided.

The decoding apparatus 300 may derive transform coefficients byperforming inverse quantization on residual information on the currentblock, that is, quantized transform coefficients (S1520).

The derived transform coefficients may be arranged according to thereverse diagonal scan order in units of 4×4 blocks, and transformcoefficients within the 4×4 block may also be arranged according to thereverse diagonal scan order. That is, the transform coefficients onwhich the inverse quantization has been performed may be arrangedaccording to a reverse scan order applied in the video codec such as inVVC or HEVC.

The decoding apparatus may derive modified transform coefficients byapplying the LFNST to the transform coefficients

The LFNST is a non-separated transform that applies the transformwithout separating the coefficients in a specific direction, unlike thefirst transform that separates and transforms the transform targetcoefficients in a vertical or horizontal direction. This non-separatedtransform may be a low-frequency non-separated transform that appliesthe forward transform only to a low-frequency region rather than theentire block region.

The LFNST index information may be received as syntax information, andthe syntax information may be received as a binarized bin stringincluding 0's and 1's.

The syntax element of the LFNST index according to the presentembodiment may indicate whether an inverse LFNST or an inversenon-separated transform is applied and any one of a transform kernelmatrix included in the transform set, and when the transform setincludes two transform kernel matrices, there may be three values of thesyntax element of the transform index.

That is, according to an embodiment, the syntax element value for theLFNST index may include 0 indicating a case in which the inverse LFNSTis not applied to the target block, 1 indicating the firsttransformation kernel matrix among the transformation kernel matrices,and 2 indicating the second transform kernel matrix among the transformkernel matrices.

The intra prediction mode information and LFNST index information may besignaled at a coding unit level.

The decoding apparatus may derive a variable indicating whether asignificant coefficient exists in the DC component of the current blockto determine whether to parse the LFNST index for the current block, andvariables may be derived based on individual transform skip flag valuesfor color components of the current block (S1530).

A variable indicating whether a significant coefficient exists in the DCcomponent of the current block may be expressed as a variableLfnstDcOnly, and for at least one transform block in one coding unit,becomes 0 when the non-zero coefficients exist at a non-DC component andbecomes 1 when the non-zero coefficients do not exist in positions otherthan DC components for all transform blocks in one coding unit. In thepresent disclosure, the DC component refers to (0, 0) or the upper leftposition as the position reference for the 2D component.

Several transform blocks may exist within one coding unit. For example,in the case of the chroma component, transform blocks for Cb and Cr mayexist, and in the case of the single tree type, the transform blocks forluma, Cb, and Cr may exist. According to an example, when a non-zerocoefficient other than the DC component position is found even in onetransform block among transform blocks constituting the current codingblock, the value of variable LnfstDcOnly may be set to 0.

Meanwhile, since the residual coding is not performed on thecorresponding transform block if non-zero coefficients do not exist inthe transform block, the variable LfnstDcOnly value is not changed bythe corresponding transform block. Therefore, if the non-zerocoefficient does not exist in the non-DC component of the transformblock, the variable LfnstDcOnly value is not changed and the previousvalue is maintained. For example, when the coding unit is coded as thesingle tree type and the variable LfnstDcOnly value is changed to 0 dueto the luma transform block, when the non-zero coefficients exist onlyin the DC component in the Cb transform block or the non-zerocoefficients do not exist in the Cb transform block, the variableLfnstDcOnly value is maintained as 0. The variable LfnstDcOnly value isinitially initialized to 1, and if no component in the current codingunit updates the variable LfnstDcOnly value to 0, it maintains the value1 as it is, and when one of the transform blocks constituting the codingunit sets the variable LfnstDcOnly value to 0, it is finally maintainedas 0.

Meanwhile, this variable LfnstDcOnly may be derived based on individualtransform skip flag values for color components of the current block.The transform skip flag for the current block may be signaled for eachcolor component, and if the tree type of the current block is a singletree, the transform skip flag value for the luma component, the variableLfnstDcOnly may be derived based on the transform skip flag value forthe luma component, the transform skip flag value for the chroma Cbcomponent, and the transform skip flag value for the chroma Crcomponent. Alternatively, if the tree type of the current block is thedual tree luma, the variable LfnstDcOnly is derived based on thetransform skip flag value for the luma component, and if the tree typeof the current block is the dual tree chroma, the variable LfnstDcOnlymay be derived based on the transform skip flag value for the chroma Cbcomponent and the transform skip flag value for the chroma Cr component.

According to an example, based on the transform skip flag value for thecolor component being 0, the variable LfnstDcOnly may indicate that asignificant coefficient exists at a position other than the DCcomponent. That is, if the tree type of the current block is a singletree, the transform skip flag value for the luma component, the variableLfnstDcOnly may be derived as 0 based on the fact that at least onevalue of the transform skip flag for the luma component, the transformskip flag value for the chroma Cb component, and the transform skip flagvalue for the chroma Cr component are 0. Alternatively, if the tree typeof the current block is the dual tree luma, the variable LfnstDcOnly isderived based on the transform skip flag value for the luma component,and if the tree type of the current block is the dual tree chroma, thevariable LfnstDcOnly may be derived based on the transform skip flagvalue for the chroma Cb component and the transform skip flag value forthe chroma Cr component.

As described above, the variable LfnstDcOnly may be initially set to 1at the coding unit level of the current block, and if the transform skipflag value is 0, the variable LfnstDcOnly may be changed to 0 at theresidual coding level.

The decoding apparatus may parse the LFNST index based on the variableLfnstDcOnly indicating that a significant coefficient exists at aposition that is not a DC component, that is, based on the variableLfnstDcOnly being 0 (S1540).

Meanwhile, in the case of the luma block to which the intrasub-partition (ISP) mode may be applied, the LFNST index may be parsedwithout deriving the variable LfnstDcOnly.

Specifically, when the ISP mode is applied and the transform_skip_flagfor the luma component, that is, the transform_skip_flag[x0][y0][0]value is 0, the tree type of the current block is a single tree or adual tree for luma, the LFNST index may be signaled regardless of thevariable LfnstDcOnly value.

On the other hand, in the case of the chroma component to which the ISPmode is not applied, the variable LfnstDcOnly value may be set to 0according to the transform_skip_flag[x0][y0][1] which is thetransform_skip_flag for the chroma Cb component andtransform_skip_flag[x0][y0][2] which is the transform_skip_flag for thechroma Cr component. That is, in the transform_skip_flag[x0][y0][cIdx],when the cIdx value is 1, only when transform_skip_flag[x0][y0][1] valueis 0, the variable LfnstDcOnly value may be set to 0, and when the cIdxvalue is 2, the transform_skip_flag[x0][y0] [2] value may be set to 0only when the transform_skip_flag[x0][y0][2] value is 0. If the variableLfnstDcOnly value is 0, the decoding apparatus may parse the LFNSTindex, otherwise the LFNST index may not be signaled and may be inferredas a value of 0.

Thereafter, the decoding apparatus may derive the modified transformcoefficients from the transform coefficients based on the LFNST indexand the LFNST matrix for LFNST (S1550).

The decoding apparatus may set a plurality of variables for the LFNSTbased on whether the LFNST index is not 0, that is, the LFNST index isgreater than 0, and the respective transform skip flag values for thecolor component are 0.

For example, in the step of applying the LFNST after parsing the LFNSTindex, the decoding apparatus may determine once again whether theindividual transform skip flag value for the color component is 0, andmay set various variables for applying the LFNST. For example, the intraprediction mode for selecting the LFNST set, the number of transformcoefficients output after applying the LFNST, the size of a block towhich the LFNST is applied, and the like may be set.

In the case of a block coded with BDPCM, the transform skip flag may beautomatically set to 1, and in this case, even if the LFNST index is not0, the transform skip flag may be 1, so when the LFNST is actuallyapplied, the transform skip flag values for each color component may bechecked again.

Alternatively, according to an example, when the flag value indicatingwhether the coded significant coefficient exists in the transform blockis 0, there may be the situation in which the transform skip flag valueis not checked. In this case as well, since it is not guaranteed thatthe transform skip flag value is 0 just because the LFNST index is not0, when the LFNST is actually applied, the transform skip flag valuesfor each color component may be checked again.

That is, the decoding apparatus may check the transform skip flag valuesfor each color component in the LFNST index parsing step, and may checkthe transform skip flag values for each color component again when theLFNST is actually applied.

The decoding apparatus may determine the LFNST set including the LFNSTmatrix based on the intra prediction mode derived from the intraprediction mode information, and select any one of a plurality of LFNSTmatrices based on the LFNST set and the LFNST index.

In this case, the same LFNST set and the same LFNST index may be appliedto the sub-partition transformation block divided in the current block.That is, since the same intra prediction mode is applied to thesub-partition transform blocks, the LFNST set determined based on theintra prediction mode may also be equally applied to all sub-partitiontransform blocks. In addition, since the LFNST index is signaled at thecoding unit level, the same LFNST matrix may be applied to thesub-partition transform block divided in the current block.

Meanwhile, as described above, the transform set may be determinedaccording to the intra prediction mode of the transform block to betransformed, and the inverse LFNST may be performed based on thetransform kernel matrix included in the transform set indicated by theLFNST index, that is, any of the LFNST matrices. A matrix applied to theinverse LFNST may be named as an inverse LFNST matrix or an LFNSTmatrix, and the name of this matrix is irrelevant as long as it has atransforce relationship with the matrix used for the forward LFNST.

In one example, the inverse LFNST matrix may be a non-square matrix inwhich the number of columns is less than the number of rows.

The decoding apparatus may derive the residual samples for the currentblock based on the primary inverse transform of the modified transformcoefficient (S1560).

In this case, as the inverse primary transform, the conventionalseparation transform may be used, and the above-described MTS may beused

Subsequently, the decoding apparatus 300 may generate reconstructedsamples based on residual samples for the current block and predictionsamples for the current block.

The following drawings were created to explain a specific example of thepresent specification. Since the names of specific devices described inthe drawings or the names of specific signals/messages/fields arepresented by way of example, the technical features of the presentspecification are not limited to the specific names used in thefollowing drawings.

FIG. 16 is a flowchart illustrating an operation of a video encodingapparatus according to an embodiment of the present disclosure.

Each step disclosed in FIG. 16 is based on some of the contentsdescribed above in FIGS. 5 to 14 . Accordingly, detailed descriptionsoverlapping with those described above in FIGS. 2 and 5 to 14 will beomitted or simplified.

The encoding apparatus 200 according to an embodiment may derive theprediction sample for the current block based on the intra predictionmode applied to the current block.

The encoding apparatus may perform prediction for each sub-partitiontransformation block when ISP is applied to the current block.

The encoding apparatus can determine whether to apply the ISP coding orthe ISP mode to the current block, that is, the coding block, anddetermine in which direction the current block is to be dividedaccording to the determination result, and derive the size and number ofdivided sub-blocks.

The same intra prediction mode is applied to the sub-partition transformblock divided from the current block, and the encoding apparatus mayderive a prediction sample for each sub-partition transform block. Thatis, the encoding apparatus sequentially performs intra prediction, forexample, horizontally or vertically, from left to right, or from top tobottom according to the division form of the sub-partition transformblocks. For the leftmost or uppermost sub-block, the reconstructed pixelof the coding block already coded is referred to as in a conventionalintra prediction method. In addition, for each side of the subsequentinternal sub-partition transformation block, when it is not adjacent tothe previous sub-partition transformation block, in order to derivereference pixels adjacent to the corresponding side, an adjacent codingblock already coded like the conventional intra prediction method refersto the reconstructed pixel.

The encoding apparatus 200 may derive residual samples for the currentblock based on the prediction samples (S1610).

The encoding apparatus 200 may derive a transform coefficient for thecurrent block by applying at least one of LFNST and MTS to the residualsamples, and may arrange the transform coefficients according to apredetermined scanning order.

The encoding apparatus may derive the transform coefficient for thecurrent block based on the primary transform for the residual sample(S1620).

The primary transform may be performed through a plurality of transformkernels like MTS, and in this case, the transform kernel may be selectedbased on the intra prediction mode.

The encoding apparatus 200 may determine whether to perform a quadratictransform or a non-separate transform, specifically LFNST, on thetransform coefficients for the current block, and apply the LFNST to thetransform coefficients to derive the modified transform coefficients.

The LFNST is a non-separated transform that applies the transformwithout separating the coefficients in a specific direction, unlike thefirst transform that separates and transforms the transform targetcoefficients in a vertical or horizontal direction. The non-separatedtransform may be a low-frequency non-separated transform that appliesthe transform only to a low-frequency region rather than the entiretarget block to be transformed.

The encoding apparatus may apply a plurality of LFNST matrices to thetransform coefficients to derive a variable indicating whether asignificant coefficient exists in the DC component of the current block,and the variables may be derived based on individual transform skip flagvalues for the color component of the current block (S1630).

The encoding apparatus may derive variables after applying LFNST to eachLFNST matrix candidate, or in a state in which LFNST is not applied whenthe LFNST is not applied.

Specifically, the encoding apparatus may apply a plurality of LFNSTcandidates, that is, the LFNST matrix to exclude the corresponding LFNSTmatrix in which the significant coefficients of all transform blocksexist only in the DC position (of course, when the CBF is 0, thecorresponding variable is excluded from the process), and compare RDvalues only between the LFNST matrices in which the variable LfnstDcOnlyvalue is 0. For example, when the LFNST is not applied, it is includedin the comparison process because it is irrelevant to the variableLfnstDcOnly value (in this case, since LFNST is not applied, thevariable LfnstDcOnly value may be determined based on the transformcoefficient obtained as a result of the primary transform) and the LFNSTmatrices with the corresponding LfnstDcOnly value of 0 are also includedin the comparison process of the RD values.

A variable indicating whether a significant coefficient exists in the DCcomponent of the current block may be expressed as a variableLfnstDcOnly, and for at least one transform block in one coding unit,becomes 0 when the non-zero coefficients exist at a non-DC component andbecomes 1 when the non-zero coefficients do not exist in positions otherthan DC components for all transform blocks in one coding unit.

Several transform blocks may exist within one coding unit. For example,in the case of the chroma component, transform blocks for Cb and Cr mayexist, and in the case of the single tree type, the transform blocks forluma, Cb, and Cr may exist. According to an example, when a non-zerocoefficient other than the DC component position is found even in onetransform block among transform blocks constituting the current codingblock, the variable LnfstDcOnly value may be set to 0.

Meanwhile, since the residual coding is not performed on thecorresponding transform block if non-zero coefficients do not exist inthe transform block, the variable LfnstDcOnly value is not changed bythe corresponding transform block. Therefore, if the non-zerocoefficient does not exist in the non-DC component of the transformblock, the variable LfnstDcOnly value is not changed and the previousvalue is maintained. For example, when the coding unit is coded as thesingle tree type and the variable LfnstDcOnly value is changed to 0 dueto the luma transform block, when the non-zero coefficients exist onlyin the DC component in the Cb transform block or the non-zerocoefficients do not exist in the Cb transform block, the variableLfnstDcOnly value is maintained as 0. The variable LfnstDcOnly value isinitially initialized to 1, and if no component in the current codingunit updates the variable LfnstDcOnly value to 0, it maintains the value1 as it is, and when one of the transform blocks constituting the codingunit sets the variable LfnstDcOnly value to 0, it is finally maintainedas 0.

Meanwhile, this variable LfnstDcOnly may be derived based on individualtransform skip flag values for color components of the current block.The transform skip flag for the current block may be signaled for eachcolor component, and if the tree type of the current block is a singletree, the transform skip flag value for the luma component, the variableLfnstDcOnly may be derived based on the transform skip flag value forthe luma component, the transform skip flag value for the chroma Cbcomponent, and the transform skip flag value for the chroma Crcomponent. Alternatively, if the tree type of the current block is thedual tree luma, the variable LfnstDcOnly is derived based on thetransform skip flag value for the luma component, and if the tree typeof the current block is the dual tree chroma, the variable LfnstDcOnlymay be derived based on the transform skip flag value for the chroma Cbcomponent and the transform skip flag value for the chroma Cr component.

According to an example, based on the transform skip flag value for thecolor component being 0, the variable LfnstDcOnly may indicate that asignificant coefficient exists at a position other than the DCcomponent. That is, if the tree type of the current block is a singletree, the transform skip flag value for the luma component, the variableLfnstDcOnly may be derived as 0 based on the fact that at least one ofthe transform skip flag value for the luma component, the transform skipflag value for the chroma Cb component, and the transform skip flagvalue for the chroma Cr component are 0. Alternatively, if the tree typeof the current block is the dual tree luma, the variable LfnstDcOnly isderived based on the transform skip flag value for the luma component,and if the tree type of the current block is the dual tree chroma, thevariable LfnstDcOnly may be derived based on the transform skip flagvalue for the chroma Cb component and the transform skip flag value forthe chroma Cr component.

As described above, the variable LfnstDcOnly may be initially set to 1at the coding unit level of the current block, and if the transform skipflag value is 0, the variable LfnstDcOnly may be changed to 0 at theresidual coding level.

The encoding apparatus may select the most optimal LFNST matrix based ona variable indicating that a significant coefficient exists at aposition other than a DC component, and may derive a modified transformcoefficient based on the selected LFNST matrix (S1640).

The encoding apparatus may set a plurality of variables for the LFNSTbased on whether the respective transform skip flag values for the colorcomponents is 0 in the step of deriving the modified transformcoefficients.

For example, after determining whether to apply the LFNST, the encodingapparatus may determine once again whether the respective transform skipflag values for the color components are 0 in the step of applying theLFNST, and may set various variables for applying the LFNST. Forexample, the intra prediction mode for selecting the LFNST set, thenumber of transform coefficients output after applying the LFNST, thesize of a block to which the LFNST is applied, and the like may be set.

In the case of the block coded by the BDPCM, since the transform skipflag may be automatically set to 1, when the LFNST is actually applied,the transform skip flag values for each color component may be checkedagain.

Alternatively, according to an example, when the flag value indicatingwhether the coded significant coefficient exists in the transform blockis 0, there may be the situation in which the transform skip flag valueis not checked. In this case as well, since it is not guaranteed thatthe transform skip flag value is 0 just because the LFNST index is not0, when the LFNST is actually applied, the transform skip flag valuesfor each color component may be checked again.

That is, the encoding apparatus may check the transform skip flag valuesfor each color component in the step of determining whether to apply theLFNST, and may check the transform skip flag values for each colorcomponent again when the LFNST is actually applied.

Meanwhile, in the case of the luma block to which the intrasub-partition (ISP) mode may be applied, the LFNST may be appliedwithout deriving the variable LfnstDcOnly.

Specifically, when the ISP mode is applied and the transform skip flagfor the luma component, that is, the transform_skip_flag[x0][y0][0]value is 0, the tree type of the current block is a single tree or adual tree for luma, the LFNST may be applied regardless of the variableLfnstDcOnly value.

On the other hand, in the case of the chroma component to which the ISPmode is not applied, the variable LfnstDcOnly value may be set to 0according to the transform_skip_flag[x0][y0][1] which is the transformskip flag for the chroma Cb component and transform_skip_flag[x0][y0][2]which is the transform skip flag for the chroma Cr component. That is,in the transform_skip_flag[x0][y0][cIdx], when the cIdx value is 1, onlywhen transform_skip_flag[x0][y0][1] value is 0, the variable LfnstDcOnlyvalue may be set to 0, and when the cIdx value is 2, thetransform_skip_flag[x0][y0] [2] value may be set to 0 only when thetransform_skip_flag[x0][y0][2] value is 0. If the variable LfnstDcOnlyvalue is 0, the encoding apparatus may apply the LFNST, otherwise theLFNST is not applied.

The encoding apparatus 200 may determine the LFNST set based on amapping relationship according to the intra prediction mode applied tothe current block, and perform the LFNST, that is, the non-separatedtransform based on one of two LFNST matrices included in the LFNST set.

In this case, the same LFNST set and the same LFNST index may be appliedto the sub-partition transformation block divided in the current block.That is, since the same intra prediction mode is applied to thesub-partition transform blocks, the LFNST set determined based on theintra prediction mode may also be equally applied to all sub-partitiontransform blocks. In addition, since the LFNST index is encoded in unitsof the coding unit, the same LFNST matrix may be applied to thesub-partition transform block divided in the current block.

As described above, the transform set may be determined according to anintra prediction mode of a transform block to be transformed. The matrixapplied to the LFNST has a transforce relationship with a matrix usedfor reverse LFNST.

In one example, the LFNST matrix may be a non-square matrix in which thenumber of rows is less than the number of columns.

The encoding apparatus may construct the image information so that theLFNST index instructing the LFNST matrix applied to the LFNST is parsedbased on the fact that the variable LfnstDcOnly is initially set to 1 inthe coding unit level of the current block, and when the transform skipflag value is 0, the variable LfnstDcOnly is changed to 0 in theresidual coding level, and the variable LfnstDcOnly is 0 (S1650).

The encoding apparatus may perform quantization based on the modifiedtransform coefficients for the current block to derive quantizedtransform coefficients, and encode an LFNST index.

That is, the encoding apparatus may generate residual informationincluding information on quantized transform coefficients. The residualinformation may include the above-described transform relatedinformation/syntax element. The encoding apparatus may encodeimage/video information including residual information and output theencoded image/video information in the form of a bitstream.

More specifically, the encoding apparatus 200 may generate informationabout the quantized transform coefficients and encode the informationabout the generated quantized transform coefficients.

The syntax element of the LFNST index according to the presentembodiment may indicate whether (inverse) LFNST is applied and any oneof the LFNST matrices included in the LFNST set, and when the LFNST setincludes two transform kernel matrices, there may be three values of thesyntax element of the LFNST index.

According to an embodiment, when a division tree structure for thecurrent block is a dual tree type, an LFNST index may be encoded foreach of a luma block and a chroma block.

According to an embodiment, the syntax element value for the transformindex may be derived as 0 indicating a case in which (inverse) LFNST isnot applied to the current block, 1 indicating a first LFNST matrixamong LFNST matrices, and 2 indicating a second LFNST matrix among LFNSTmatrices.

In the present disclosure, at least one of quantization/dequantizationand/or transform/inverse transform may be omitted. Whenquantization/dequantization is omitted, a quantized transformcoefficient may be referred to as a transform coefficient. Whentransform/inverse transform is omitted, the transform coefficient may bereferred to as a coefficient or a residual coefficient, or may still bereferred to as a transform coefficient for consistency of expression.

In addition, in the present disclosure, a quantized transformcoefficient and a transform coefficient may be referred to as atransform coefficient and a scaled transform coefficient, respectively.In this case, residual information may include information on atransform coefficient(s), and the information on the transformcoefficient(s) may be signaled through a residual coding syntax.Transform coefficients may be derived based on the residual information(or information on the transform coefficient(s)), and scaled transformcoefficients may be derived through inverse transform (scaling) of thetransform coefficients. Residual samples may be derived based on theinverse transform (transform) of the scaled transform coefficients.These details may also be applied/expressed in other parts of thepresent disclosure.

In the above-described embodiments, the methods are explained on thebasis of flowcharts by means of a series of steps or blocks, but thepresent disclosure is not limited to the order of steps, and a certainstep may be performed in order or step different from that describedabove, or concurrently with another step. Further, it may be understoodby a person having ordinary skill in the art that the steps shown in aflowchart are not exclusive, and that another step may be incorporatedor one or more steps of the flowchart may be removed without affectingthe scope of the present disclosure.

The above-described methods according to the present disclosure may beimplemented as a software form, and an encoding apparatus and/ordecoding apparatus according to the disclosure may be included in adevice for image processing, such as, a TV, a computer, a smartphone, aset-top box, a display device or the like.

When embodiments in the present disclosure are embodied by software, theabove-described methods may be embodied as modules (processes, functionsor the like) to perform the above-described functions. The modules maybe stored in a memory and may be executed by a processor. The memory maybe inside or outside the processor and may be connected to the processorin various well-known manners. The processor may include anapplication-specific integrated circuit (ASIC), other chipset, logiccircuit, and/or a data processing device. The memory may include aread-only memory (ROM), a random access memory (RAM), a flash memory, amemory card, a storage medium, and/or other storage device. That is,embodiments described in the present disclosure may be embodied andperformed on a processor, a microprocessor, a controller or a chip. Forexample, function units shown in each drawing may be embodied andperformed on a computer, a processor, a microprocessor, a controller ora chip.

Further, the decoding apparatus and the encoding apparatus to which thepresent disclosure is applied, may be included in a multimediabroadcasting transceiver, a mobile communication terminal, a home cinemavideo device, a digital cinema video device, a surveillance camera, avideo chat device, a real time communication device such as videocommunication, a mobile streaming device, a storage medium, a camcorder,a video on demand (VoD) service providing device, an over the top (OTT)video device, an Internet streaming service providing device, athree-dimensional (3D) video device, a video telephony video device, anda medical video device, and may be used to process a video signal or adata signal. For example, the over the top (OTT) video device mayinclude a game console, a Blu-ray player, an Internet access TV, a Hometheater system, a smartphone, a Tablet PC, a digital video recorder(DVR) and the like.

In addition, the processing method to which the present disclosure isapplied, may be produced in the form of a program executed by acomputer, and be stored in a computer-readable recording medium.Multimedia data having a data structure according to the presentdisclosure may also be stored in a computer-readable recording medium.The computer-readable recording medium includes all kinds of storagedevices and distributed storage devices in which computer-readable dataare stored. The computer-readable recording medium may include, forexample, a Blu-ray Disc (BD), a universal serial bus (USB), a ROM, aPROM, an EPROM, an EEPROM, a RAM, a CD-ROM, a magnetic tape, a floppydisk, and an optical data storage device. Further, the computer-readablerecording medium includes media embodied in the form of a carrier wave(for example, transmission over the Internet). In addition, a bitstreamgenerated by the encoding method may be stored in a computer-readablerecording medium or transmitted through a wired or wirelesscommunication network. Additionally, the embodiments of the presentdisclosure may be embodied as a computer program product by programcodes, and the program codes may be executed on a computer by theembodiments of the present disclosure. The program codes may be storedon a computer-readable carrier.

Claims disclosed herein can be combined in a various way. For example,technical features of method claims of the present disclosure can becombined to be implemented or performed in an apparatus, and technicalfeatures of apparatus claims can be combined to be implemented orperformed in a method. Further, technical features of method claims andapparatus claims can be combined to be implemented or performed in anapparatus, and technical features of method claims and apparatus claimscan be combined to be implemented or performed in a method.

1. An image decoding method performed by a decoding apparatus,comprising: receiving residual information through a bitstream; derivingtransform coefficients for a current block based on the residualinformation; deriving modified transform coefficients by applying a lowfrequency non-separable transform (LFNST) to the transform coefficients;deriving residual samples for the current block based on an inverseprimary transform for the modified transform coefficients; andgenerating a reconstructed picture based on the residual samples,wherein the deriving the modified transform coefficients includes:deriving a variable indicating whether a significant coefficient existsonly in a DC component of the current block; and parsing an LFNST indexbased on the variable indicating that the significant coefficient existsat a position other than the DC component, and wherein the variable isderived based on an individual transform_skip_flag value for a colorcomponent of the current block.
 2. The image decoding method of claim 1,wherein the variable indicates that the significant coefficient existsat a position other than the DC component based on thetransform_skip_flag value for the color component being
 0. 3. The imagedecoding method of claim 2, wherein the variable is initially set to 1in a coding unit level of the current block, wherein based on thetransform_skip_flag value being 0, the variable is changed to 0 in aresidual coding level, and wherein the LFNST index is parsed based onthe variable being
 0. 4. The image decoding method of claim 1, whereinthe transform_skip_flag for the current block is signaled for each colorcomponent.
 5. The image decoding method of claim 1, wherein the derivingthe modified transform coefficients further includes: setting aplurality of variables for the LFNST based on whether the LFNST index isnot 0 and the individual transform_skip_flag value for the colorcomponent is
 0. 6. The image decoding method of claim 1, wherein basedon a tree type of the current block being a single tree, the variable isderived based on the transform skip flag value for a luma component, thetransform_skip_flag value for a chroma Cb component, and thetransform_skip_flag value for a chroma Cr component.
 7. The imagedecoding method of claim 1, wherein based on a tree type of the currentblock being dual tree luma, the variable is derived based on thetransform skip flag value for a luma component.
 8. The image decodingmethod of claim 1, wherein based on a tree type of the current blockbeing dual tree chroma, the variable is derived based on the transformskip flag value for a chroma Cb component and the transform_skip_flagvalue for a chroma Cr component.
 9. An image encoding method performedby an image encoding apparatus, comprising: deriving prediction samplesfor a current block; deriving residual samples for the current blockbased on the prediction samples; deriving transform coefficients for thecurrent block based on a primary transform for the residual samples;applying an LFNST to derive modified transform coefficients from thetransform coefficients; generating residual information based on themodified transform coefficients; and encoding image informationincluding the residual information, wherein the applying the LFNST toderive the modified transform coefficients includes: selecting an LFNSTmatrix among a plurality of LFNST matrices; and applying the LFNST tothe transform coefficients based on the selected LFNST matrix to derivethe modified transform coefficients, wherein the image informationincludes an LFNST index based on a variable indicating that asignificant coefficient exists at a position other than a DC componentof the current block, and wherein the variable is derived based on anindividual transform_skip_flag value for a color component of thecurrent block.
 10. The image encoding method of claim 9, wherein thevariable indicates that the significant coefficient exists at a positionother than the DC component based on the transform_skip_flag value forthe color component being
 0. 11. The image encoding method of claim 10,wherein the variable is initially set to 1 in a coding unit level of thecurrent block, wherein based on the transform_skip_flag value being 0,the variable is changed to 0 in a residual coding level, and wherein theimage information includes the LFNST index based on the variable being0.
 12. The image encoding method of claim 9, wherein the applying theLFNST includes setting a plurality of variables for the LFNST based onwhether the individual transform_skip_flag value for the color componentis
 0. 13. The image encoding method of claim 9, wherein based on a treetype of the current block being a single tree, the variable is derivedbased on the transform_skip_flag value for a luma component, thetransform_skip_flag value for a chroma Cb component, and thetransform_skip_flag value for a chroma Cr component.
 14. The imageencoding method of claim 9, wherein based on a tree type of the currentblock being dual tree luma, the variable is derived based on thetransform_skip_flag value for a luma component, and based on a tree typeof the current block being dual tree chroma, the variable is derivedbased on the transform_skip_flag value for a chroma Cb component and thetransform skip flag value for a chroma Cr component.
 15. Anon-transitory computer-readable digital storage medium storing abitstream generated by an image encoding method, the method comprising:deriving prediction samples for a current block; deriving residualsamples for the current block based on the prediction samples; derivingtransform coefficients for the current block based on a primarytransform for the residual samples; applying an LFNST to derive modifiedtransform coefficients from the transform coefficients; generatingresidual information based on the modified transform coefficients; andencoding image information including the residual information to outputthe bitstream, wherein the applying the LFNST to derive the modifiedtransform coefficients includes: selecting an LFNST matrix among aplurality of LFNST matrices; and applying the LFNST to the transformcoefficients based on the selected LFNST matrix to derive the modifiedtransform coefficients, wherein the image information includes an LFNSTindex based on a variable indicating that a significant coefficientexists at a position other than a DC component, and wherein the variableis derived based on an individual transform_skip_flag value for a colorcomponent of the current block.